Nonlinear Analysis: Modelling and Control
type: channel
description: Founded in 1997 and dedicated to publishing interdisciplinary works on nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature. Indexed in the Scopus (Q2) database since 2009 and in the Web of Science (Q1) database since 2010.
publisher: Vilnius University Press
language: en
publication name: Nonlinear Analysis: Modelling and Control
issn: 1392-5113
copyright: Please read the Copyright Notice in Journal Policy.
items: Observer-based distributed optimization for linear multiagent systems with external disturbances
items: Existence and stability results for triple systems of fractional Sturm–Liouville–Langevin equations with cyclic boundary conditions
items: Energetic formulation of the subgroup commutativity degree
items: Nonparametric changed segment detection in functional data
items: Modeling the impact of detritus-based irrigation on agricultural crop production
items: New strong convergence algorithms for general equilibrium and variational inequality problems and resolvent operators in Banach spaces
items: Editorial Board
items: Dynamical investigation of the nonlinear Schrödinger equation with second-order spatiotemporal involvement of the time-conformable operator
items: Fundamental contractions in suprametric spaces
items: Monotone iterative sequences for positive solutions of a p-Laplacian Hadamard fractional boundary value problem on an unbounded domain
items: Exact controllability of conformable linear systems with semilinear boundary control
items: Relative controllability of damped fractional differential system with distributed delays and impulses
items: An analytical study of the time-fractional extended shallow-water wave equation in (3 + 1)-dimension with two different derivatives and their comparison
items: Quantization-based event-triggered control for synchronization of 2-D discrete-time switched master-slave systems in Roesser model
items: Null controllability of Chafee–Infante equation under discrete-time point measurements
items: Trajectory controllability of semilinear dynamic systems on time scales
items: On the h-manifolds for impulsive conformable neural networks with reaction–diffusion terms
items: Synchronization analysis for stochastic multi-layer networks: Event-based impulsive control with predefined impulsive intervals
items: An advanced visualization of self-organizing maps by determining data clusters
items: Boundary value problems for third-order differential equations involving singular Phi-Laplacian operators
items: Spatiotemporal dynamics of a modified Leslie–Gower predator–prey model: Effects of diffusion and taxis-driven movements on pattern formation
items: Arnold tongues of divergence in the Caputo fractional standard map of nilpotent matrices
items: Generalizations of Darbo’s fixed point-theorem and its application to the solvability of a nonlinear fractional differential equation
items: Exploring fixed points via admissibility criteria for fuzzy theta f-weak contractions
items: Existence of nontrivial solutions for a class of 2n-order ODE
items: A new dynamic model for simultaneous saccharification and fermentation process of rice wine
items: Efficient computation of blood velocity in the left atrial appendage: A practical perspective
items: Background risk model in presence of heavy tails under dependence
items: Stability analysis of leptospirosis compartmental model with impact of contaminated environment
items: Finite-time synchronization and quasi-synchronization of fractional-order fuzzy BAM neural networks with time delays

Observer-based distributed optimization for linear multiagent systems with external disturbances
type: item
description: This paper addresses the distributed optimization problem in linear multiagent systems (MASs) under external disturbances. Firstly, an observation system is designed by utilizing the output values of agents, which can eliminate external disturbances of system. Secondly, an event-triggered control algorithm is proposed through the gradient information of local cost functions, and its convergence is rigorously established using the Lyapunov stability and looped functional theory. This novel event-triggered protocol incorporates dwell time within the threshold function, effectively eliminating Zeno behavior. By leveraging the looped functional technique, more relaxed conditions are derived for solving the distributed optimization problem. Finally, the validity and feasibility of the proposed protocol are substantiated through numerical simulation.
subject: Articles
  topic: section
subject: external disturbances
  topic: keywords
subject: multiagent system
  topic: keywords
subject: distributed optimization
  topic: keywords
subject: looped functional method
  topic: keywords
creator: Xuening Xu
creator: Zhiyong Yu
creator: Haijun Jiang
rights: Copyright (c) 2026 Xuening Xu | Zhiyong Yu | Haijun Jiang https://creativecommons.org/licenses/by/4.0
date: 2026-01-07
publication date: 2026-01-07
starting page: 1
ending page: 19
doi: 10.15388/namc.2026.31.44762

Existence and stability results for triple systems of fractional Sturm–Liouville–Langevin equations with cyclic boundary conditions
type: item
description: We investigate a triple system of fractional Sturm–Liouville–Langevin equations with cyclic antiperiodic boundary conditions. The fixed point theorem serves as a tool to establish the existence and uniqueness criteria for solutions. By applying the Banach contraction principle, we also obtain the Ulam–Hyers stability of the proposed system. Finally, examples are provided to illustrate main results.
subject: Articles
  topic: section
subject: fractional Sturm–Liouville–Langevin equation
  topic: keywords
subject: triple system
  topic: keywords
subject: existence and uniqueness
  topic: keywords
subject: Ulam-types stability
  topic: keywords
creator: Gang Chen
creator: Zhanbing Bai
creator: Wei Zhang
rights: Copyright (c) 2026 Gang Chen | Zhanbing Bai | Wei Zhang https://creativecommons.org/licenses/by/4.0
date: 2026-01-05
publication date: 2026-01-05
starting page: 1
ending page: 26
doi: 10.15388/namc.2026.31.44744

Energetic formulation of the subgroup commutativity degree
type: item
description: Finite groups in which every pair of subgroups (H, K) satisfies H K = K H have been classified by Iwasawa, but only in the last decade it was introduced the notion of subgroup commutativity degree sd(G) of groups G. From restrictions of numerical nature on sd(G) one usually derives structural conditions on G; in fact, among groups G with sd(G) = 1, one finds those originally studied by Iwasawa. Here we offer a new perspective of study for sd(G); we use a recently introduced graph, which is called nonpermutability graph of subgroups ΓL(G) of G, in order to restrict sd(G) via the notion of energy of ΓL(G) and by means of methods of spectral graph theory. In particular, we find new criteria of nilpotence for G along with new bounds for sd(G).
subject: Articles
  topic: section
subject: spectral graph theory
  topic: keywords
subject: energy of a graph
  topic: keywords
subject: subgroup commutativity degree
  topic: keywords
subject: nonpermutability graph of subgroups
  topic: keywords
subject: adjacency matrix
  topic: keywords
creator: Seid Kassaw Muhie
creator: Daniele Ettore Otera
creator: Francesco G. Russo
rights: Copyright (c) 2026 Seid Kassaw Muhie | Daniele Ettore Otera | Francesco G. Russo https://creativecommons.org/licenses/by/4.0
date: 2026-01-01
publication date: 2026-01-01
starting page: 212
ending page: 236
doi: 10.15388/namc.2026.31.44490

Nonparametric changed segment detection in functional data
type: item
description: We address the epidemic change point detection problem without parametric assumptions. We propose statistics based on Cramér–von Mises-type statistic and reproducing kernel Hilbert space that iterate through all interval subsets, rescaling them to remain sensitive to both short and long epidemics. We prove limit theorems and provide quantiles for both statistics under the different parametrizations. The simulations show consistent power across a wide range of scenarios, and an application to electricity balancing prices consistently detects a market disturbance.
subject: Articles
  topic: section
subject: epidemic change
  topic: keywords
subject: reproducing kernel Hilbert space
  topic: keywords
subject: Cramér–von Mises-type statistic
  topic: keywords
creator: Karolis Bartkus
creator: Alfredas Račkauskas
rights: Copyright (c) 2026 Karolis Bartkus | Alfredas Račkauskas https://creativecommons.org/licenses/by/4.0
date: 2026-01-01
publication date: 2026-01-01
starting page: 194
ending page: 211
doi: 10.15388/namc.2026.31.44489

Modeling the impact of detritus-based irrigation on agricultural crop production
type: item
description: The excessive use of chemical fertilizers in agricultural farms poses a serious threat to nearby water bodies, such as lakes, ponds, etc., by causing algal blooms in these water bodies and also put agricultural sustainability at risk. This study deals with the use of algae-rich pond water for irrigation, which impacts soil fertility through organic detritus. A nonlinear mathematical model is formulated to analyze the ecological and agronomic impacts of this irrigation approach. The formulation of the model takes into account that the detritus-based pond water used for irrigation initially benefits the crop growth; but once it exceeds a certain threshold, reduces the crop yield. Furthermore, the model demonstrates how nature-based solutions can be strategically integrated into agricultural system to achieve long-term resilience. The study identifies key thresholds and behavioral transitions by detecting a saddle-node, transcritical, and Hopf bifurcations within the proposed mathematical model. To support analytical findings, we conduct numerical simulations that provide a strong evidence of the agricultural ecosystem’s resilience particularly in maintaining the crop yield under the modeled irrigation conditions. These simulations underscore the potential for managing detritus density to optimize crop productivity while minimizing ecological risks. Findings of this study can support the environment-friendly irrigation policies suited to different agroecological regions. Study reveals that detritus-based irrigation promotes crop productivity up to a critical threshold of detritus input, beyond which its effects turn inhibitory. Simultaneously, it suppresses algal blooms, thereby uncovering a natural self-regulating mechanism with significant implications for sustainable irrigation practices and nutrient management policies.
subject: Articles
  topic: section
subject: mathematical model
  topic: keywords
subject: agriculture
  topic: keywords
subject: algae
  topic: keywords
subject: detritus
  topic: keywords
subject: bifurcations
  topic: keywords
creator: Arvind Kumar Misra
creator: Prinsi Shukla
rights: Copyright (c) 2026 Arvind Kumar Misra | Prinsi Shukla https://creativecommons.org/licenses/by/4.0
date: 2026-01-05
publication date: 2026-01-05
starting page: 1
ending page: 23
doi: 10.15388/namc.2026.31.44411

New strong convergence algorithms for general equilibrium and variational inequality problems and resolvent operators in Banach spaces
type: item
description: In this paper, we introduce two new algorithms for solving variational inequalities in Banach spaces. Our aim is finding a common element of the solution set of variational inequalities (for two inverse-strongly monotone operators) and an equilibrium problem and the set of fixed points of two relatively nonexpansive mappings and a family of resolvent operators. Then the strong convergence of the sequences generated by these algorithms to this element will be proved under suitable conditions. Finally, we provide a numerical example to illustrate our main results.
subject: Articles
  topic: section
subject: relatively nonexpansive mapping
  topic: keywords
subject: fixed point problem
  topic: keywords
subject: equilibrium problem
  topic: keywords
subject: inverse-strongly monotone operator
  topic: keywords
subject: maximal monotone operator
  topic: keywords
creator: Mostafa Ghadampour
creator: Ebrahim Soori
creator: Ravi P. Agarwal
creator: Donal O’Regan
rights: Copyright (c) 2026 Mostafa Ghadampour | Ebrahim Soori | Ravi P. Agarwal | Donal O’Regan https://creativecommons.org/licenses/by/4.0
date: 2026-01-05
publication date: 2026-01-05
starting page: 1
ending page: 25
doi: 10.15388/namc.2026.31.44410

Editorial Board
type: item
subject: Front Matter
  topic: section
subject: Editorial Board
  topic: keywords
creator: Artūras Štikonas
rights: Copyright (c) 2026 Artūras Štikonas https://creativecommons.org/licenses/by/4.0
date: 2026-01-01
publication date: 2026-01-01
starting page: 1
ending page: 1
doi: 10.15388/

Dynamical investigation of the nonlinear Schrödinger equation with second-order spatiotemporal involvement of the time-conformable operator
type: item
description: The article analyzes the application of the extended hyperbolic function technique to a conformable-operator nonlinear Schrödinger equation, incorporating group velocity dispersion coefficients and second-order spatiotemporal components. The primary objective is establishing a spectrum of solutions directly pertinent to optical fibers. The extracted results, which include bright, singular, straddled, dark-bright, and dark solitons, are obtained by hyperbolic and trigonometric function-type solutions. We exhibit contour plots with two-dimensional and three-dimensional visualizations to emphasize the implication of the proposed conformable-operator nonlinear Schrödinger equation and to depict the diverse novel optical solutions. Additionally, we study the impact of the conformable operator on these solutions, employing graphical analysis to demonstrate its implications. The governing model shows potential applications in transmitting ultra-fast pulses via optical fibers.
subject: Articles
  topic: section
subject: extended hyperbolic function method
  topic: keywords
subject: second-order spatiotemporal terms
  topic: keywords
subject: group velocity dispersion coefficients
  topic: keywords
subject: nonlinear conformable Schrödinger equation
  topic: keywords
subject: optical fibers
  topic: keywords
creator: Muhammad Amin S. Murad
creator: Faraidun Kadir Hamasalh
creator: Mujahid Iqbal
creator: Sandeep Malik
creator: Ahmed H. Arnous
rights: Copyright (c) 2026 Muhammad Amin S. Murad | Faraidun Kadir Hamasalh | Mujahid Iqbal | Sandeep Malik | Ahmed H. Arnous https://creativecommons.org/licenses/by/4.0
date: 2026-01-01
publication date: 2026-01-01
starting page: 178
ending page: 193
doi: 10.15388/namc.2026.31.44291

Fundamental contractions in suprametric spaces
type: item
description: In this manuscript, we propose the notion of a strong extended s-suprametric space, a novel extension that outperforms both s-suprametric and extended suprametric spaces. It looks into the aspects of open and closed ball topologies within this structure. It also investigates the concepts of existence and uniqueness using basic contractions viz. Banach and Kannan contractions. Illustrative examples demonstrate how the strong extended s-suprametric space outperforms its extended equivalent. Our examples demonstrate the presence and distinctness of fixed points in this scenario. Furthermore, exploiting these newly launched results, the manuscript investigates the analysis of a boundary value problem, including diffusing chemical material constrained between parallel walls with related concentrations at the boundaries, taking into account supplied raw density and recognized absorbing coefficients. It also applies these insights to a nonlinear boundary value issue involving satellite web coupling in which a thin sheet joins two cylindrical spacecraft. This coupling causes nonlinearity, resulting in a separate boundary value issue influenced by radiation effects within the satellites.
subject: Articles
  topic: section
subject: strong extended s-suprametric space
  topic: keywords
subject: Banach contraction principle
  topic: keywords
subject: diffusing chemical material
  topic: keywords
subject: satellite web coupling
  topic: keywords
creator: Saad Jamhan Aldosari
creator: Haroon Ahmad
creator: Mudasir Younis
creator: Mahpeyker Öztürk
creator: Farwa Asmat
rights: Copyright (c) 2026 Saad Jamhan Aldosari | Haroon Ahmad | Mudasir Younis | Mahpeyker Öztürk | Farwa Asmat https://creativecommons.org/licenses/by/4.0
date: 2026-01-01
publication date: 2026-01-01
starting page: 160
ending page: 177
doi: 10.15388/namc.2026.31.44253

Monotone iterative sequences for positive solutions of a p-Laplacian Hadamard fractional boundary value problem on an unbounded domain
type: item
description: In this paper, we ensure the existence and uniqueness of positive solutions for a Hadamard fractional boundary value problem with the p-Laplacian operator on an unbounded domain. The problem is formulated as a nonlinear differential equation involving a fractional derivative of order ℓ ∈ (n – 1, n], n ∈ N, along with boundary conditions of the Hadamard fractional integral and derivative. Using the monotone iterative technique, we establish the existence of positive solutions by constructing monotone sequences that approach the solution. An error estimation formula is provided. An example is also discussed to illustrate the main result.
subject: Articles
  topic: section
subject: existence results
  topic: keywords
subject: infinite interval
  topic: keywords
subject: fractional derivative
  topic: keywords
creator: Fulya Yoruk Deren
creator: Tugba Senlik Cerdik
creator: Ravi P. Agarwal
rights: Copyright (c) 2026 Fulya Yoruk Deren | Tugba Senlik Cerdik | Ravi P. Agarwal https://creativecommons.org/licenses/by/4.0
date: 2026-01-01
publication date: 2026-01-01
starting page: 131
ending page: 159
doi: 10.15388/namc.2026.31.44238

Exact controllability of conformable linear systems with semilinear boundary control
type: item
description: In this manuscript, we investigate the exact controllability of a class of linear systems governed by conformable fractional derivatives of order α in (0; 1] subject to semilinear boundary control in Banach spaces. We first establish the existence of mild solutions to the associated fractional Cauchy problems. We then derive sufficient conditions ensuring the exact controllability of these conformable linear systems under semilinear boundary control actions. An abstract model of an age-structured population dynamics system is provided to illustrate the applicability of the theoretical results.
subject: Articles
  topic: section
subject: conformable derivative
  topic: keywords
subject: controllability
  topic: keywords
subject: fixed point theorem
  topic: keywords
subject: semilinear boundary control
  topic: keywords
subject: fractional semigroups
  topic: keywords
creator: Abdellah Lourini
creator: Mohamed El Azzouzi
creator: Mohamed Laabissi
rights: Copyright (c) 2026 Abdellah Lourini | Mohamed El Azzouzi | Mohamed Laabissi https://creativecommons.org/licenses/by/4.0
date: 2026-01-01
publication date: 2026-01-01
starting page: 110
ending page: 130
doi: 10.15388/namc.2026.31.44149

Relative controllability of damped fractional differential system with distributed delays and impulses
type: item
description: In this paper, we deal with the relative controllability of linear and nonlinear damped fractional differential system with distributed delays and impulses. The sufficient and necessary conditions for the relative controllability of the linear system under consideration are given by using the controllability Gramian matrix. We also prove a sufficient condition on the nonlinear term to ensure that the above system is relative controllable. Two instances are provided to verify that our theoretical results are accurate.
subject: Articles
  topic: section
subject: relative controllability
  topic: keywords
subject: fractional calculus
  topic: keywords
subject: distributed delays
  topic: keywords
subject: impulses
  topic: keywords
subject: Mittag-Leffler function
  topic: keywords
creator: Wangmin An
creator: Danfeng Luo
rights: Copyright (c) 2026 Wangmin An | Danfeng Luo https://creativecommons.org/licenses/by/4.0
date: 2026-01-01
publication date: 2026-01-01
starting page: 93
ending page: 109
doi: 10.15388/namc.2026.44133

An analytical study of the time-fractional extended shallow-water wave equation in (3 + 1)-dimension with two different derivatives and their comparison
type: item
description: In ocean physics, an essential mathematical framework for examining the dynamic behavior of waves is the (3 + 1)-dimensional generalized shallow-water wave equation. This approach is driven by the growing need to incorporate nonlinear and anomalous behaviors in shallow-water wave propagation into more realistic mathematical models. This motivation is a key consideration for improving coastal hazard prediction, mitigating tsunami impacts, optimizing renewable energy extraction, and deepening our understanding of complex coastal processes. In this paper, exact solutions of the fractional generalized shallow-water wave equation are constructed using two alternative methods: the extended modified auxiliary equation mapping method and the F-expansion approach. The extended modified auxiliary equation mapping method yielded nineteen exact solutions across two main sets, while the F-expansion method produced solutions for seventeen different cases. To visualize these, 2D and 3D graphical representations have been generated for several solutions using fractional parameter values α ∈ (0; 1], including sample values such as 0.2, 0.5, 0.7, and 0.78, to illustrate how the order of the derivative affects the soliton profile. The results show that decreasing α leads to broader and smoother soliton structures. Finally, the modulation instability of the governing model is also investigated, confirming that the established results are stable.
subject: Articles
  topic: section
subject: the extended modified auxiliary equation mapping method
  topic: keywords
subject: the F-expansion method
  topic: keywords
subject: M-truncated derivative
  topic: keywords
subject: beta-derivative
  topic: keywords
subject: shallow-water wave equation
  topic: keywords
subject: modulation instability
  topic: keywords
creator: Esra Ünal Yılmaz
creator: Yeçim Sağlam Özkan
rights: Copyright (c) 2026 Esra Ünal Yılmaz | Yeçim Sağlam Özkan https://creativecommons.org/licenses/by/4.0
date: 2026-01-01
publication date: 2026-01-01
starting page: 68
ending page: 92
doi: 10.15388/namc.2026.31.44130

Quantization-based event-triggered control for synchronization of 2-D discrete-time switched master-slave systems in Roesser model
type: item
description: This paper investigates synchronization control for 2-D discrete-time switched master-slave systems modeled by the Roesser framework, which is classic for spatiotemporal dynamics in 2-D systems. A novel quantization-based event-triggered control strategy is proposed to handle complexities from switching dynamics, discrete-time features, and spatial coupling, while considering limited communication resources. By designing a mode-dependent event-triggered strategy and constructing mode-dependent Lyapunov functions for horizontal and vertical dynamics, new sufficient conditions are derived to ensure global exponential synchronization (GES) of the system. The approach relaxes strict stability requirements for individual modes, allowing global stability even with unstable modes. Additionally, the integration of quantization techniques and event-triggered mechanisms significantly reduces data transmission, thereby optimizing network bandwidth usage. Numerical simulations verify the method’s effectiveness.
subject: Articles
  topic: section
subject: 2-D switched systems
  topic: keywords
subject: event-triggered control
  topic: keywords
subject: quantization
  topic: keywords
subject: synchronization
  topic: keywords
subject: stability
  topic: keywords
creator: Zhimin Zhou
creator: Lei Shi
creator: Wenbo Liu
creator: Xilong Luo
creator: Shiqi Mo
creator: Jiayin Mou
rights: Copyright (c) 2026 Zhimin Zhou | Lei Shi | Wenbo Liu | Xilong Luo | Shiqi Mo | Jiayin Mou https://creativecommons.org/licenses/by/4.0
date: 2026-01-01
publication date: 2026-01-01
starting page: 45
ending page: 67
doi: 10.15388/namc.2026.31.44128

Null controllability of Chafee–Infante equation under discrete-time point measurements
type: item
description: Nonlinear system is one of the main research objects in cybernetics, and it is the main theme of cybernetics in the 21st century. Recently, the control of the reaction–diffusion equation has been widely studied, but the nonlinear reaction–diffusion equation has been rarely studied. This paper will take the Chafee–Infante equation as an example, and the null controllability of this equation will be shown. We consider the null controllability for Chafee–Infante equation with point actuations subject to a known constant delay. The point measurements can be sampled in time and transmitted through a communication network with a time-varying delay. We design an observer for the future value of the state in order to compensate the input delay, then we ensure that the estimation error vanishes exponentially with a desired decay rate by using a time-varying observer gain. By constructing Lyapunov–Krasovskii functional and combining linear matrix inequalities (LIMs), we obtain the convergence conditions. We design the boundary controller and the point controller, and we conclude that both controllers can ensure the exponential stability of the closed-loop system with an arbitrary decay rate, which is smaller than that of the observers estimation error. At last, numerical example is given.
subject: Articles
  topic: section
subject: Chafee–Infante reaction–diffusion equation
  topic: keywords
subject: point control
  topic: keywords
subject: boundary control
  topic: keywords
subject: input delay
  topic: keywords
creator: Shuai Guo
creator: Yuan Yuan Qin
creator: Guangying Lv
creator: Guang-an Zou
rights: Copyright (c) 2026 Shuai Guo | Yuan Yuan Qin | Guangying Lv | Guang-an Zou https://creativecommons.org/licenses/by/4.0
date: 2026-01-01
publication date: 2026-01-01
starting page: 25
ending page: 44
doi: 10.15388/namc.2026.31.44003

Trajectory controllability of semilinear dynamic systems on time scales
type: item
description: This paper explores the trajectory controllability of semilinear dynamic systems defined over time scales, which is an important aspect in understanding and manipulating the behavior of such systems across discrete and continuous domains. We address the controllability of these systems under the assumption that the nonlinearities satisfy a Lipschitz-type condition. Our approach involves a detailed analysis of how these conditions impact the ability to steer the system’s state along a desired trajectory within a finite-time horizon. We establish sufficient conditions for trajectory controllability (T-controllability), providing a theoretical framework that extends classical results from differential and difference equations to the broader context of time-scale calculus. To illustrate the practical implications of our theoretical findings, we include several numerical examples that demonstrate the application of our results to specific semilinear dynamic systems, highlighting the versatility and effectiveness of our approach.
subject: Articles
  topic: section
subject: T-controllability
  topic: keywords
subject: Lipschitz condition
  topic: keywords
subject: regressive
  topic: keywords
subject: rd-continuous
  topic: keywords
subject: Delta-differentiable
  topic: keywords
subject: Delta-Carathéodory condition
  topic: keywords
creator: Sakthivel Shivasivapriyaa
creator: Shanmugasundaram Karthikeyan
creator: Venkatesan Govindaraj
creator: Dimplekumar Chalishajar
rights: Copyright (c) 2026 Sakthivel Shivasivapriyaa | Shanmugasundaram Karthikeyan | Venkatesan Govindaraj | Dimplekumar Chalishajar https://creativecommons.org/licenses/by/4.0
date: 2026-01-01
publication date: 2026-01-01
starting page: 1
ending page: 24
doi: 10.15388/namc.2026.31.43981

On the h-manifolds for impulsive conformable neural networks with reaction–diffusion terms
type: item
description: In this paper, we consider a new class of conformable impulsive reaction–diffusion neural networks. The stable behavior of h-manifolds with respect to the model is investigated, and sufficient conditions are proposed by constructing suitable Lyapunov-like functions. Our results are new and contribute to the development of the theory of impulsive conformable models. Examples are also presented to illustrate the proposed criteria.
subject: Articles
  topic: section
subject: conformable derivatives
  topic: keywords
subject: neural networks
  topic: keywords
subject: reaction–diffusion terms
  topic: keywords
subject: practical stability
  topic: keywords
subject: impulses
  topic: keywords
subject: h-manifolds
  topic: keywords
creator: Anatoliy Martynyuk
creator: Gani Stamov
creator: Ivanka Stamova
rights: Copyright (c) 2025 Anatoliy Martynyuk | Gani Stamov | Ivanka Stamova https://creativecommons.org/licenses/by/4.0
date: 2025-10-23
publication date: 2025-10-23
starting page: 1211
ending page: 1231
doi: 10.15388/namc.2025.30.43844

Synchronization analysis for stochastic multi-layer networks: Event-based impulsive control with predefined impulsive intervals
type: item
description: This article explores the novel approach to addressing the intra/inter-layer synchronization challenges in stochastic multi-layer networks (SMLNs). First, considering the influence of time delay in control, an event-triggered delayed impulsive control (ETDIC) strategy is developed, where the impulsive instant is determined by the predesigned event-triggered mechanism. Moreover, by introducing piecewise auxiliary functions, it effectively excludes Zeno behavior within the ETDIC framework. The study then derives sufficient conditions for ensuring intra- and inter-layer; synchronization, leveraging the Lyapunov method and rigorous mathematical analysis. Finally, theoretical results are validated through numerical simulations.
subject: Articles
  topic: section
subject: stochastic multi-layer networks
  topic: keywords
subject: intra-layer synchronization
  topic: keywords
subject: inter-layer synchronization
  topic: keywords
subject: event-triggered delayed impulsive control
  topic: keywords
creator: Hengyu Liu
creator: Jiarong Li
creator: Haijun Jiang
creator: Jinling Wang
creator: Cheng Hu
rights: Copyright (c) 2025 Hengyu Liu | Jiarong Li | Haijun Jiang | Jinling Wang | Cheng Hu https://creativecommons.org/licenses/by/4.0
date: 2025-10-20
publication date: 2025-10-20
starting page: 1186
ending page: 1210
doi: 10.15388/namc.2025.30.43839

An advanced visualization of self-organizing maps by determining data clusters
type: item
description: This paper proposes a novel approach to improve the visualization capabilities of self-organizing maps and facilitate the identification of the resulting clusters. Unlike other clustering algorithms, self-organizing maps lack the feature to select a predefined number of clusters, and the boundaries of the clusters are not explicitly represented on the self-organizing maps. The main advantage of our proposed approach is that the option for selecting the desired number of clusters has been implemented. The experimental investigation was performed using four datasets with different characteristics. The improved visualization leverages various similarity distances to assess their impact on performance. The effectiveness of the novel approach to clustering results has been compared with those of the well-known k-means and hierarchical clustering methods, which allow for the selection of the desired number of clusters. Additionally, the visualization results, obtained by the proposed approach, were compared with those produced using the Orange Data Mining tool, where the u-matrix is applied to visualize a self-organizing map. The advantage of our approach compared to the u-matrix visualization has been highlighted in this paper. The performance of clustering algorithms has been measured by calculating the ratio of data items correctly assigned to clusters in the case when the clusters are predefined in the analyzed dataset. The results obtained showed that the most effective similarity distances are the cosine and correlation distances, which help to detect the correctly predefined clusters in the visualization of self-organizing maps.
subject: Articles
  topic: section
subject: self-organizing maps
  topic: keywords
subject: u-matrix
  topic: keywords
subject: similarity distances
  topic: keywords
subject: visualization
  topic: keywords
subject: data clustering
  topic: keywords
subject: number of clusters
  topic: keywords
creator: Pavel Stefanovič
creator: Olga Kurasova
rights: Copyright (c) 2025 Pavel Stefanovič | Olga Kurasova https://creativecommons.org/licenses/by/4.0
date: 2025-10-14
publication date: 2025-10-14
starting page: 1163
ending page: 1185
doi: 10.15388/namc.2025.30.43803

Boundary value problems for third-order differential equations involving singular Phi-Laplacian operators
type: item
description: We study strongly nonlinear, third-order differential equations of type (Φ(k(t)u''(t)))' = f(t, u(t), u'(t), u''(t)), a.e. t ∈ J, where Φ is the singular Φ-Laplacian operator. That is, Φ : (–r, r) -> R, r > 0, is a generic strictly increasing homeomorphism with bounded domain, which generalizes the relativistic operator Φ(u) := u (r2 – u2)–1/2. Moreover, k is a nonnegative continuous function, which can vanish on a set of zero measure, so such equations can be singular, and f is a general Carathédory function. For these equations, we investigate boundary value problems both in compact intervals (when J = [a; b]) and in a half-line (with J = [a;+∞)), and we prove existence results under mild assumptions. Our approach is based on fixed point techniques.
subject: Articles
  topic: section
subject: boundary value problems on unbounded domains
  topic: keywords
subject: heteroclinic solutions
  topic: keywords
subject: nonlinear differential operators
  topic: keywords
subject: singular Phi-Laplacian operator
  topic: keywords
subject: singular equation
  topic: keywords
creator: Alessandro Calamai
creator: Francesca Papalini
rights: Copyright (c) 2025 Alessandro Calamai | Francesca Papalini https://creativecommons.org/licenses/by/4.0
date: 2025-10-10
publication date: 2025-10-10
starting page: 1145
ending page: 1162
doi: 10.15388/namc.2025.30.43775

Spatiotemporal dynamics of a modified Leslie–Gower predator–prey model: Effects of diffusion and taxis-driven movements on pattern formation
type: item
description: In this manuscript, we investigate a Leslie–Gower predator–prey model with Crowley–Martin-type functional response. We also explore the dynamics of reaction–diffusion as well as reaction–diffusion–advection model. Specifically, our study focuses on an ecological model involving a generalist predator that induces fear, has carry-over effects, and experiences competitive interference. For the temporal model, a detailed mathematical analysis is carried out, investigating the positivity and boundedness of the solutions. We observe both monostability and bistability phenomena, and explore various local and global bifurcations by varying the fear and carry-over parameters. Interestingly, the fear and its carry-over effects have opposing roles in influencing stability within the temporal model. We incorporated prey-taxis into a general reaction–diffusion framework to represent the directed movement of predators towards regions with higher prey densities or when tracking signals such as scent to locate their prey. We perform the complete analysis of diffusion-driven and taxis-driven instability for reaction–diffusion and reaction–diffusion–advection models, respectively. Our findings emphasize the significant influence of predator diffusion and prey-taxis on pattern formation, revealing that increased random predator movement, combined with a moderate level of prey-taxis, can stabilize the model.
subject: Articles
  topic: section
subject: fear effect
  topic: keywords
subject: carry-over effect
  topic: keywords
subject: bifurcations
  topic: keywords
subject: prey-taxis
  topic: keywords
subject: Turing pattern
  topic: keywords
creator: Anand Singh
creator: Sayan Mandal
creator: Pankaj Kumar Tiwari
creator: Balram Dubey
rights: Copyright (c) 2025 Anand Singh | Sayan Mandal | Pankaj Kumar Tiwari | Balram Dubey https://creativecommons.org/licenses/by/4.0
date: 2025-10-10
publication date: 2025-10-10
starting page: 1121
ending page: 1144
doi: 10.15388/namc.2025.30.43767

Arnold tongues of divergence in the Caputo fractional standard map of nilpotent matrices
type: item
description: Arnold tongues of divergence in the Caputo fractional standard map of nilpotent matrices are explored in this paper. The scalar iterative variables in the Caputo fractional standard map are replaced by iterative matrix variables. The divergence effects induced by the nilpotent matrices result in specific patterns of Arnold tongues. Automatic machine classification techniques help to identify different types of Arnold tongues according to the dynamics of the transient processes of the system. Computational experiments are used to validate theoretical insights and to reveal the patterns of Arnold tongues of divergence.
subject: Articles
  topic: section
subject: Arnold tongue
  topic: keywords
subject: Caputo fractional standard map
  topic: keywords
subject: nilpotent, divergence
  topic: keywords
creator: Ugnė Orinaitė
creator: Rasa Šmidtaitė
creator: Minvydas Ragulskis
rights: Copyright (c) 2025 Ugnė Orinaitė | Rasa Šmidtaitė | Minvydas Ragulskis https://creativecommons.org/licenses/by/4.0
date: 2025-10-07
publication date: 2025-10-07
starting page: 1103
ending page: 1120
doi: 10.15388/namc.2025.30.43746

Generalizations of Darbo’s fixed point-theorem and its application to the solvability of a nonlinear fractional differential equation
type: item
description: This paper introduces novel fixed-point theorems for generalized Proinov contraction mappings utilizing the measure of noncompactness. These results significantly extend existing contraction principles and provide novel methods for analyzing nonlinear problems. We demonstrate the practical power of our theorems by establishing the existence of solutions to a broad class of nonlinear fractional differential equations with integral boundary conditions. An illustrative example underscores the effectiveness of our approach, promising impactful applications in fractional calculus and nonlinear analysis. Overall, these results enrich the theoretical framework and offer valuable insights for researchers working on complex dynamical systems and applied mathematical models.
subject: Articles
  topic: section
subject: Proinov-type contraction
  topic: keywords
subject: measure of noncompactness
  topic: keywords
subject: fractional differential equation
  topic: keywords
creator: Maha Belhadj
creator: Jamal Rezaei Roshan
creator: Stojan Stojan Radenović
rights: Copyright (c) 2025 Maha Belhadj | Jamal Rezaei Roshan | Stojan Stojan Radenović https://creativecommons.org/licenses/by/4.0
date: 2025-10-07
publication date: 2025-10-07
starting page: 1081
ending page: 1102
doi: 10.15388/namc.2025.30.43745

Exploring fixed points via admissibility criteria for fuzzy theta f-weak contractions
type: item
description: In this study, we introduce a new class of fuzzy contractions, called fuzzy α-η-θf -weak contractions, and establish fixed point results within the framework of complete fuzzy metric spaces. A fuzzy metric space generalizes the concept of a metric space by defining the “distance” between two points ω and υ using a function ϑ(ω, υ, ς) that quantifies the degree of nearness between these points for a parameter ς > 0. This parameter ς reflects various factors influencing the closeness of the points, making fuzzy metric spaces a powerful tool for modeling uncertainty and imprecision in mathematical contexts. Based on this framework, we prove several fixed point theorems addressing the existence and uniqueness of fixed points for such contractions. By carefully selecting specific forms of the functions θf, α, and η, our primary results can be adapted to yield a variety of significant corollaries. Furthermore, our findings leverage admissible and auxiliary functions to provide a broader framework that consolidates, extends, and refines existing results in fixed point theory.
subject: Articles
  topic: section
subject: fixed point theory
  topic: keywords
subject: fuzzy metric
  topic: keywords
subject: contractions mapping
  topic: keywords
subject: admissible functions
  topic: keywords
subject: theta f-weak contraction
  topic: keywords
creator: Abdelhamid Moussaoui
rights: Copyright (c) 2025 Abdelhamid Moussaoui https://creativecommons.org/licenses/by/4.0
date: 2025-10-07
publication date: 2025-10-07
starting page: 1067
ending page: 1080
doi: 10.15388/namc.2025.30.43744

Existence of nontrivial solutions for a class of 2n-order ODE
type: item
description: We consider a semilinear 2n-order problem with nonconstant coefficients. We deduce existence results by using variational methods in two directions. We primarily treat the existence when the nonlinearity has asymptotic linear behaviour at infinity and is either asymptotically sublinear or linear at zero. Secondly, we discuss the superlinear case at infinity and prove three existence results showing that our problem has at least one or two nonzero solutions.
subject: Articles
  topic: section
subject: higher-order equations
  topic: keywords
subject: variational methods
  topic: keywords
subject: critical points
  topic: keywords
creator: Antonia Chinnì
creator: Cristian-P. Danet
creator: Beatrice Di Bella
rights: Copyright (c) 2025 Antonia Chinnì | Cristian-P. Danet | Beatrice Di Bella https://creativecommons.org/licenses/by/4.0
date: 2025-10-07
publication date: 2025-10-07
starting page: 1048
ending page: 1066
doi: 10.15388/namc.2025.30.43742

A new dynamic model for simultaneous saccharification and fermentation process of rice wine
type: item
description: In this paper, a new fractional model for the simultaneous saccharification and fermentation process of rice wine is proposed. To begin with, the existence and uniqueness of solution to the new model are proved by using some fixed point theorems. In addition, the stability at the equilibrium point and the Ulam–Hyers stability of the fractional simultaneous and saccharification fermentation model are analyzed. Then the approximate solutions of the fractional simultaneous saccharification and fermentation model are obtained by using the generalised Euler method. Finally, numerical simulations are given to verify the rationality of the fractional simultaneous saccharification and fermentation model. The new model proposed in this paper can more sensitively capture changes in the reaction.
subject: Articles
  topic: section
subject: simultaneous saccharification and fermentation
  topic: keywords
subject: fixed point theorem
  topic: keywords
subject: stability analysis
  topic: keywords
subject: generalized Euler method
  topic: keywords
subject: numerical simulation
  topic: keywords
creator: Li Wang
creator: Lihong Zhang
creator: Tingting Guan
rights: Copyright (c) 2025 Li Wang | Lihong Zhang | Tingting Guan https://creativecommons.org/licenses/by/4.0
date: 2025-10-07
publication date: 2025-10-07
starting page: 1031
ending page: 1047
doi: 10.15388/namc.2025.30.43741

Efficient computation of blood velocity in the left atrial appendage: A practical perspective
type: item
description: The goal of the paper is to present the FSI (fluid-structure interaction) CFD (computational fluid dynamics) simulations of the blood flow in the LA (left atrium) for patient-specific geometry of the left atrium appendage (LAA). These simulations are important for the decision making in cardiology and cardiac surgery of the patients with atrial fibrillation. Nowadays according current atrial fibrillation treatment guidelines, initiation of oral anticoagulant therapy is recommended for patients with a CHA2DS2–VASc score greater or equal to 2 for males, and greater or equal to 3 for females, for lowering stroke risk. This therapy although has undesirable effects and provokes bleeding in a part of cases. That is why it is important to detect the stagnation zones of the blood flow in LAA. The presence of such zones justifies the necessity of the anticoagulant therapy. The FSI CFD simulations in the heart is a challenging problem: the existing softwares are not too robust for real life Reynolds numbers and often do not converge to the solution of the Navier–Stokes equations for the blood coupled with the elasticity equations of the wall. That is why we first provide the CFD computations with the rigid wall when the codes are more stable. Using this solution as a source of parameters for the implicit numerical scheme solver, we then provide the FSI computations, which become much more robust.
subject: Articles
  topic: section
subject: Navier–Stokes equations
  topic: keywords
subject: fluid structure interaction
  topic: keywords
subject: mathematical modeling
  topic: keywords
subject: computer simulations
  topic: keywords
creator: Audrius Aidietis
creator: Sigita Aidietienė
creator: Oleg Ardatov
creator: Sergejus Borodinas
creator: Rimgaudas Katkus
creator: Kristina Kaulakytė
creator: Nikolajus Kozulinas
creator: Grigory Panasenko
creator: Konstantinas Pileckas
creator: Gediminas Račkauskas
rights: Copyright (c) 2025 Audrius Aidietis | Sigita Aidietienė | Oleg Ardatov | Sergejus Borodinas | Rimgaudas Katkus | Kristina Kaulakytė | Nikolajus Kozulinas | Grigory Panasenko | Konstantinas Pileckas | Gediminas Račkauskas https://creativecommons.org/licenses/by/4.0
date: 2025-10-07
publication date: 2025-10-07
starting page: 1011
ending page: 1030
doi: 10.15388/namc.2025.30.43740

Background risk model in presence of heavy tails under dependence
type: item
description: In this paper, we examine two problems on applied probability, which are directly connected with the dependence in presence of heavy tails. The first problem is related to max-sum equivalence of the randomly weighted sums in bivariate setup. Introducing a new dependence, called generalized tail asymptotic independence, we establish the bivariate max-sum equivalence under a rather general dependence structure when the primary random variables follow distributions from the intersection of the dominatedly varying and the long-tailed distributions. Based on this max-sum equivalence, we provide a result about the asymptotic behavior of two kinds of ruin probabilities over a finite-time horizon in a bivariate renewal risk model with constant interest rate. The second problem is related to the asymptotic behavior of the tail distortion risk measure in a static portfolio called background risk model. In opposite to other approaches on this topic, we use a general enough assumption that is based on multivariate regular variation.
subject: Articles
  topic: section
subject: joint tail behavior
  topic: keywords
subject: randomly weighted sums
  topic: keywords
subject: tail distortion risk measure
  topic: keywords
subject: bivariate renewal risk model
  topic: keywords
subject: interdependence
  topic: keywords
subject: multivariate regular variation
  topic: keywords
creator: Dimitrios G. Konstantinides
creator: Charalampos D. Passalidis
rights: Copyright (c) 2025 Dimitrios G. Konstantinides | Charalampos D. Passalidis https://creativecommons.org/licenses/by/4.0
date: 2025-08-12
publication date: 2025-08-12
starting page: 982
ending page: 1010
doi: 10.15388/namc.2025.30.42995

Stability analysis of leptospirosis compartmental model with impact of contaminated environment
type: item
description: The main objective of this article is to analyse the stability properties of a model involving humans, animals and contaminated environment. As a first step, the model is formulated, and its biological well-posedness is proved. Then the basic reproduction number is derived using the next generation matrix (NGM) method. The local and global asymptotic stability of the system at the disease free and endemic equilibrium points are also established. Finally, numerical simulations to illustrate the validity of the theoretical results are performed.
subject: Articles
  topic: section
subject: leptospirosis
  topic: keywords
subject: free-living pathogen
  topic: keywords
subject: next-generation matrix method
  topic: keywords
subject: basic reproduction number
  topic: keywords
subject: stability analysis
  topic: keywords
creator: Mohandas Sooryadas
creator: Abdul Latheef Haseena
creator: Selvan Selsha
creator: Krishnan Balachandran
rights: Copyright (c) 2025 Mohandas Sooryadas | Abdul Latheef Haseena | Selvan Selsha | Krishnan Balachandran https://creativecommons.org/licenses/by/4.0
date: 2025-08-07
publication date: 2025-08-07
starting page: 957
ending page: 981
doi: 10.15388/namc.2025.30.42973

Finite-time synchronization and quasi-synchronization of fractional-order fuzzy BAM neural networks with time delays
type: item
description: This paper concentrates on the finite-time synchronization (FTS) and the quasi-synchronization (QS) problems for a kind of fractional-order fuzzy BAM neural networks with time delays (FOFBAMNNs). In order to reach the goals of synchronization, two novel controllers are designed. Then, based on finite-time stability theorem, Lyapunov function theory, and several inequality techniques, through the application of two different designed controllers, several criteria for both FTS and QS are established. Moreover, more precise error level and settling times are given. The effectiveness of the derived criteria is ultimately validated through two simulations.
subject: Articles
  topic: section
subject: finite-time synchronization
  topic: keywords
subject: quasi-synchronization
  topic: keywords
subject: BAM neural networks
  topic: keywords
subject: Caputo derivative
  topic: keywords
subject: fuzzy term.
  topic: keywords
creator: Wei Zhao
creator: Hongmei Zhang
creator: Hai Zhang
creator: Qinyun Lu
creator: Jinde Cao
rights: Copyright (c) 2025 Wei Zhao | Hongmei Zhang | Hai Zhang | Qinyun Lu | Jinde Cao https://creativecommons.org/licenses/by/4.0
date: 2025-07-30
publication date: 2025-07-30
starting page: 936
ending page: 956
doi: 10.15388/namc.2025.30.42902