Nonlinear Analysis: Modelling and Control
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.
Please read the Copyright Notice in Journal Policy.
Global asymptotic synchronization for delayed inertial BAM neural networks without controllers via the fundamental solution matrix method
This paper considers the global asymptotic synchronization (GAS) for master-slave delayed inertial bidirectional associative memory (BAM) neural networks (NNs). Most existing studies on GAS rely on the LMI approach, integral inequality, matrix measure, and maximum-valued methods, usually with additional controllers. In contrast, this work achieves GAS without using the above methods or designing any controllers. Instead, two new sufficient conditions are derived via the fundamental solution matrix method for first-order differential systems. For the first time, the fundamental solution matrix method is introduced to deal with the GAS for the NNs.
master-slave inertial BAM neural networks
Copyright (c) 2026 Yiping Shuai | Zhengqiu Zhang | Zhibin Dai https://creativecommons.org/licenses/by/4.0
On the dynamics of the autonomous Duffing–Holmes oscillator
The autonomous Duffing–Holmes oscillator ẋ = y, ẏ = x – x3 + by – kz, ż = w(y – z), depending on the three parameters b, k, and w, has been studied previously by several authors who showed that for certain parameter values, it exhibits chaotic motion, or that numerically it has two periodic orbits coming from a Hopf bifurcation, or that it can have three equilibria for some given values of the parameters. Here we provide new results on the integrability and the global dynamics of the autonomous Duffing–Holmes oscillator using its first integrals and Darboux invariants when these exist for some given values of its parameters.
Copyright (c) 2026 Érika Diz-Pita | Jaume Jaume Llibre | M. Victoria Otero-Espinar https://creativecommons.org/licenses/by/4.0
Volatility is a key measure of financial risk, and GARCH models are widely used to describe its dynamics. However, they do not account for the influence of news sentiment, which can significantly shape market volatility. Recently proposed News-Augmented GARCH model addresses it by incorporating sentiment signals in a nonlinear, asymmetric, and multiplicative form. This paper examines its theoretical properties and performs a simulation-based hyperparameter study. The analysis establishes the existence of a unique and causal solution, derives a stability condition, and evaluates model sensitivity and parameter recovery under controlled scenarios. Results demonstrate robust performance across various settings and provide guidance for informed hyperparameter selection and evaluation, enhancing model’s reliability for empirical applications.
Copyright (c) 2026 Diana Vereškaitė | Jurgita Markevičiūtė | Andrius Buteikis https://creativecommons.org/licenses/by/4.0
Enhanced chaotic maps for sustainable cryptographic security
We propose a comparative study of chaotification techniques that enhance the complexity of one-dimensional maps for sustainable cryptographic applications. Specifically, we examine the use of modulo operation, remainder operation, and k-deep-zoom (k-DZ) transformation applied to the sine map. Each technique’s effectiveness is analyzed using bifurcation diagrams, Lyapunov exponents, and correlation results. Additionally, the statistical performance of the techniques is assessed using the NIST SP 800-22 battery of tests, and the computational efficiency is evaluated in terms of the number of operations. The study aims to identify the best chaotification method for generating robust pseudorandom bit generators (PRBGs) suitable for secure encryption and sustainable cryptography.
Copyright (c) 2026 Nasr-Eddine Mellah | Samir Ladaci | Murilo S. Baptista | Celso Grebogi https://creativecommons.org/licenses/by/4.0
Computational technique for robust dynamic optimization of fractional impulsive switched systems
In this work, we study a robust dynamic optimization problem for nonlinear fractional impulsive switched systems (FISSs) with uncertain parameters. The main novelty lies in directly incorporating parameter sensitivity into the cost functional to enhance robustness against model uncertainty. To solve the resulting problem, the system sensitivity is first computed through an auxiliary FISS, and a time-scaling transformation is employed to reformulate the optimization over fixed switching instants. Tractable gradient expressions are then derived using a set of auxiliary systems. A gradient-based optimization method is subsequently developed to solve the transformed problem together with a numerical scheme tailored for the FISSs. Two numerical examples demonstrate that the proposed technique achieves effective optimization performance and improved robustness.
Copyright (c) 2026 Zhaohua Gong | Benchawan Wiwatanapataphee | Chongyang Liu | Yonghong Wu https://creativecommons.org/licenses/by/4.0
Joint ruin probability and risk contagion measure in a quota-share reinsurance risk model
Consider a quota-share reinsurance risk model with constant premiums and stochastic returns in which an insurer purchases fixed-proportion quota-share reinsurance for its business line. Both the insurer and reinsurer may engage in risk-free investments, with their nonnegative general (not necessarily Lévy) log-price processes following an arbitrary dependence structure. Under the assumption that claim sizes are pairwise strongly quasiasymptotically independent and follow heavy-tailed distributions, this paper derives asymptotic formulas for two types of finite-time joint ruin probabilities and for a risk contagion measure from the insurer to the reinsurer. Furthermore, we conduct numerical studies to verify the accuracy of the derived asymptotic results, using the Monte Carlo method combined with an explicit order-3.0 weak scheme.
Copyright (c) 2026 Yang Yang | Rongshan Huang | Hui Meng https://creativecommons.org/licenses/by/4.0
Positive solutions for a fourth-order integral boundary value problem involving impulses and the p-Laplacian
In this paper, we investigate the existence of positive solutions for a fourth-order integral boundary value problem involving impulses and the p-Laplacian operator. First, we construct a linear operator that incorporates impulsive effects, and then analyze its spectral radius properties. Subsequently, under suitable conditions on the spectral radius, we apply the fixed point index theory to establish existence theorems for the problem. Our results cover cases where the nonlinear term exhibits (p – 1)-superlinear/sublinear growth, and the impulsive term satisfies superlinear/sublinear growth conditions.
fourth-order integral boundary value problem
Copyright (c) 2026 Jiafa Xu | Zhichun Yang | Donal O’Regan | Jiangdong Liao https://creativecommons.org/licenses/by/4.0
Existence of positive solutions for tempered fractional differential equations with p-Laplacian operator
This paper investigates the existence of positive solutions for a specific category of p-Laplacian tempered fractional differential equations in which the nonlinear term f contains an integral operator θ. By employing fixed point theorems for sum operators in partially ordered Banach spaces, together with Krasnosel’skii fixed point theorem, the existence of positive solutions is established. Moreover, iterative sequences are constructed to approximate the unique positive solution of the problem. Finally, three examples are presented to illustrate the main results.
Copyright (c) 2026 Jiqiang Jiang | Minghui Liu | Lishan Liu | Yonghong Wu https://creativecommons.org/licenses/by/4.0
Existence and approximate controllability results for time-fractional stochastic Navier–Stokes equations
This paper deals with time-fractional stochastic Navier–Stokes equations, which are characterized by the coexistence of stochastic noise and a fractional power of the Laplacian. We establish sufficient conditions for the existence and approximate controllability of a unique mild solution to time-fractional stochastic Navier–Stokes equations. Using a fixed point technique, we first demonstrate the existence and uniqueness of a mild solution to the equation under consideration. We then establish approximate controllability results by using the concepts of fractional calculus, semigroup theory, functional analysis, and stochastic analysis.
Copyright (c) 2026 Renu Chaudhary | Simeon Reich | Juan. J. Nieto https://creativecommons.org/licenses/by/4.0
Controllability and Ulam–Hyers stability analysis of conformable fractional differential systems with time delays and impulsive effects
We investigate the controllability and Ulam–Hyers stability of a class of conformable fractional differential systems with time delays and impulsive effects. Specifically, we analyze the movement rules before and after the impulse, utilizing both the Banach and Schauder fixed point theorem to derive controllability. Furthermore, we employ nonlinear functional analysis methods to study Ulam–Hyers stability. To demonstrate the applicability and feasibility of our main conclusions, an illustrative example is provided.
Copyright (c) 2026 Luchao Zhang | Xiping Liu | Mei Jia | Zhensheng Yu | Changxiang He https://creativecommons.org/licenses/by/4.0
Existence, uniqueness and averaging principle for fractional Dirichlet boundary value problems driven by Rosenblatt process and Lévy jumps
We address the existence, uniqueness, and averaging principle for Caputo–Hadamard fractional dynamic systems with Dirichlet boundary conditions driven by Rosenblatt process and pure Lévy jumps. First, Lemma 4 establishes the equivalent integral equation representation of our system. Using this foundation, existence and uniqueness are proved by Banach's contraction principle under stochastic calculus, Lipschitz and finite energy conditions. Subsequently, under appropriate averaging assumptions, the system is averaged out with time scale ϵ. Mean-square convergence between original solution and its counterpart is verified by employing tools such as Wiener–Itô double integral, Cauchy–Schwarz, Doob's martingale, and Gronwall–Bellman inequalities. Eventually, computational example with numerical simulations is provided to support the theoretical results.
Copyright (c) 2026 Jalisraj Arokiyanathan | Ramalingam Udhayakumar https://creativecommons.org/licenses/by/4.0
Fixed-time distributed formation control for nonlinear heterogeneous multiagent systems subject to input nonlinearities and actuator faults
This work focuses on distributed practical fixed-time formation (PFTF) control for heterogeneous multiagent systems (MASs) with inherent nonlinear dynamics, coupled input nonlinearities, and potential actuator faults. Conventional backstepping methods face the challenge of “differential explosion”. To resolve this issue, we propose an innovative command filtering strategy with fixed-time convergence properties, integrated with a compensating mechanism that also ensures fixed-time suppression of filtering errors. Leveraging the synergy of fixed-time control theory, backstepping recursion, and neural networks function approximation, a distributed PFTF control protocol is developed. The designed scheme ensures that the MASs attain the predefined formation configuration within a fixed time, while driving all errors converge to a small residual set. Numerical simulations validate the effectiveness and performance of the proposed approach.
Copyright (c) 2026 Jianmin Jiao | Junmin Li | Chao He | Rui Zhang https://creativecommons.org/licenses/by/4.0
Adaptive fixed-time control with prescribed performance for nonlinear networked control systems under deception attacks
This paper presents a novel fixed-time adaptive control scheme with prescribed performance for nonlinear networked control systems (NCSs) under deception attacks. The Nussbaum function is first employed to tackle the challenge of unknown attack weights and their signs. A hybrid approach integrating a fixed-time performance function with a nonlinear shifting function is used to mitigate the influence of initial conditions on tracking errors. Furthermore, a sufficient condition is derived to guarantee the practical fixed-time stability of NCSs, even in the face of deception attacks. Finally, the effectiveness of the proposed methodology is demonstrated through a mass-spring-damper system simulation.
Copyright (c) 2026 Linfang Shao | Weiwei Sun | Lusong Ding https://creativecommons.org/licenses/by/4.0
Synchronization of quaternion-valued BAM neural networks with time-varying delays
This paper studies the global asymptotic synchronization (GAS) and global exponential synchronization (GES) problems of a class of quaternion-valued bidirectional associative memory neural networks (QVBAMNNs) with time-varying delays. Based on the matrix measure approach and Halanay inequality, sufficient conditions for GAS of unbounded time-varying delay system and GES of bounded time-varying delay system were established. Different from existing methods, this approach does not require the construction of Lyapunov functions and obtains the criteria for system synchronization expressed in terms of norms and measures. Finally, the validity of the proposed theoretical results and the feasibility of the control strategy are verified through numerical simulations.
Copyright (c) 2026 Lu Li | Zhengwen Tu | Tao Peng | Bing Chen | Jiang Xiong | Liangwei Wang https://creativecommons.org/licenses/by/4.0
Evaluation of domain-specific convolutional neural network layers for galaxy classification tasks
Due to increasing amount of data, galaxy image classification is being automated using machine learning, with the most common approach being convolutional neural networks (CNNs). Using domain-specific observations about galaxy morphology, we propose two CNN layers – Focal and Wave. The Focal layer highlights information in the center, while the Wave layer is designed to highlight spiral arms. A comprehensive evaluation of layers is performed using datasets of 4 and 11 (not yet deeply studied) galaxy types, with and without augmentations. With no augmentations, our models outperform best results of models used in other studies with Wilcoxon signed-rank test's p-value of pF1 = 0.002 for both 4 and 11 classes in terms of F1 score (used to better evaluate performance due to inherent class imbalance). Moreover, our layers help reduce overfitting and reliance on augmentation combinations, as our models, despite benefiting less from augmentations, still achieve results comparable to other augmented models. Additionally, our models tuned for 4-class data perform equally well on 11-class data, and vice versa. Finally, an ensemble of our models trained without augmentations achieves comparable results to our augmented models.
Copyright (c) 2026 Tomas Mūžas | Andrius Vytautas Misiukas Misiūnas | Tadas Meškauskas https://creativecommons.org/licenses/by/4.0
Adaptive synchronization of quaternion-valued inertial neural networks with uncertain parameters and a flexible time delay
In this paper, a direct method is presented for analyzing the adaptive synchronization of quaternion-valued inertial neural networks (QVINNs) with uncertain parameters and time delay. By this method, the forms of time delays and the Lyapunov function in this paper are flexible, and in stability analysis, the requirement for negative definiteness of Lyapunov functions will be weakened. In addition, a more generalized adaptive synchronization controller has been proposed for QVINNs, which no longer requires multiple calculations of the control gain. Since most of the previous adaptive control methods did not impose requirements on the convergence speed of the QVINNs, a class of improved adaptive controllers is designed to address the slow synchronization speed of QVINNs. Finally, numerical simulations are conducted to validate the synchronization conditions.
Copyright (c) 2026 Xufan Yin | Tao Peng | Jiang Xiong | Zhengwen Tu | Zuxiong Li | Liangwei Wang https://creativecommons.org/licenses/by/4.0
Exponential synchronization of quaternion-valued switching neural networks with mixed delays
This paper investigates the exponential synchronization problem for a class of quaternion-valued switching neural networks (QVSNNs) with mixed time delays and sampled-data control. By using a Lyapunov function method involving sampling instants, sufficient conditions for the synchronization of the considered neural networks (NNs) are obtained in the form of linear matrix inequalities (LMIs). It is worth emphasizing that this paper reduces the conservativeness of stability criteria by combining the free-weight matrix method with discrete sampling points; moreover, the derived criteria are valid for both quaternion-valued and nonasynchronous switching NNs. Finally, the feasibility of the proposed approach is verified by two numerical examples.
quaternion-valued switching neural networks
Copyright (c) 2026 Wei Tan | Yongxiang Zhao | Tao Peng | Zhengwen Tu | Yuan Dong https://creativecommons.org/licenses/by/4.0
Prescribed-time leader-following scaled consensus for nonlinear multiagent systems
In this paper, the leader-following (L-F) scaled consensus (SC) for first-order multiagent systems (MASs) is considered within a prescribed time (PT). First, a distributed control protocol is proposed by incorporating a time-varying gain function and scaled factors. This protocol is designed to drive the states of the leader and followers to a predefined scaled relationship within the PT. It is worth noting that, by appropriately selecting the scaled factor, the protocol can also achieve complete consensus, bipartite consensus, or cluster consensus among the agents. To further enhance the control performance and reduce communication frequency, an improved control protocol is proposed by incorporating an event-triggered mechanism in which the event-triggering function is constructed using time-varying variables. Moreover, based on the PT stability theory, sufficient conditions are derived to ensure that SC is achieved within the PT. Finally, the effectiveness of the proposed control protocol is verified through two numerical simulation examples.
Copyright (c) 2026 Chongjiao Qian | Zhiyong Yu | Haijun Jiang https://creativecommons.org/licenses/by/4.0
An open-source parallel algorithm of Bayesian-based global search with Hooke–Jeeves local refinement for multi-objective optimization problems
Contemporary engineering and scientific problems often involve computationally intensive optimization tasks. This paper proposes a parallel version of the hybrid algorithm of the previously proposed Bayesian-based global search with Hooke–Jeeves local refinement for multi-objective optimization problems. The Bayesian-based hybrid algorithm has been complemented with multi-process data exchange using Open MPI to obtain a scalable parallel application. Each parallel process executes the Bayesian-based hybrid algorithm, and at the end, the Pareto optimal solutions of each process are merged into an aggregated set of Pareto optimal solutions. The master-slave pattern was used to parallelize the computations, where slave processes execute optimization algorithm and then send the obtained Pareto optimal solutions to the master process, which, in turn, also executes optimization algorithm and merges the Pareto optimal solutions of all processes. The developed parallel algorithm was tested under the same conditions previously used for testing other Bayesian algorithms to enable comparison of performance. Finally, the proposed parallel algorithm was published on the GitHub developer platform for code sharing.
Copyright (c) 2026 Linas Litvinas https://creativecommons.org/licenses/by/4.0
Entropy generation for MHD pulsating stratified liquid flow between two permeable beds
In natural systems such as lakes, reservoirs, and the upper ocean layers, temperature-induced stratified fluid flows are frequently observed. Numerous studies have explored key aspects of these flows, including stability, mixing, and thermal transport. However, the heat transfer characteristics of stratified fluid flow between permeable beds remain unexplored. This study aims to address this gap by performing an entropy generation analysis of pulsating stratified fluid flow between two permeable beds, with key applications in geothermal energy extraction, environmental modelling, and biomedical engineering. Liquid is injected through the lower bed and extracted from the upper bed at an equal velocity. The governing flow equations are solved numerically using the fourth-order Runge–Kutta (RK-4) method in combination with the shooting method in Mathematica. Graphical results are presented to illustrate the influence of key parameters on velocity, temperature, Nusselt number, entropy generation, Bejan number, mass flux, and stress distribution. Our results indicated that a rise in the Reynolds number, pressure gradient, and stratification parameter boosts the fluid velocity, while a higher slip parameter tends to reduce it. The temperature distribution declines with the rise of magnetic field and Reynolds number. In contrast, it intensifies with elevated Brinkman number, pressure gradient, and stratification parameter.
Copyright (c) 2026 Madhurya Vangalapudi | Suripeddi Srinivas https://creativecommons.org/licenses/by/4.0
Exact solutions of stochastic generalized long–short wave resonance equations with cubic–quintic nonlinearity via the new sub-ODE method
We study a stochastic generalized long–short wave resonance system with cubic–quintic nonlinearities, perturbation terms, and multiplicative white noise in the Itô sense. Using a traveling-wave reduction combined with the newly proposed sub-ODE method, we construct explicit families of solitary-wave and elliptic-function solutions, including elevation, depression, and singular branches. The analysis reveals how stochastic effects shrink the existence domains of these solutions, while a Hamiltonian linearization provides Vakhitov–Kolokolov- and Grillakis–Shatah–Strauss-type stability criteria. The results enrich nonlinear wave theory and offer insights relevant to solitary-wave applications in fiber optics and related technologies.
Copyright (c) 2026 Elsayed M.E. Zayed | Basel M.M. Saad | Mir Sajjad Hashemi | Muhammad Amin S. Murad | Ahmed H. Arnous | Mustafa Bayram https://creativecommons.org/licenses/by/4.0
Improved fixed-time consensus of delayed nonlinear leader–follower multi-agent systems
This article aims to study the problem of fixed-time consensus for nonlinear leader–follower multi-agent systems (MASs) with time delay. Firstly, a new fixed-time stability lemma is derived, where the condition of inequality contains a time-delayed term. Furthermore, a more precise estimated value of settling time (ST) including delayed parameter is obtained, which is different from those existing fixed-time stability lemmas. Thereby, it provides some options for designers in many practical scenarios when considering the delayed systems. Secondly, for the purpose of explaining its applicability, fixed-time consensus of leader–follower nonlinear MASs is investigated by designing a nonlinear control protocol including constant time delay. The designed protocol not only guarantees fixed-time consensus but also effectively improves the convergence rate. With the new proposed lemma, a novel consensus criterion is designed. This is the first time to obtain the time-delayed dependent fixed-time stability criterion for MASs. Finally, the validity and superiority of the established theoretical results are confirmed by one numerical simulation.
Copyright (c) 2026 Mingqiang Meng | Qintao Gan | Ruihong Li | Luke Li | Qiaokun Kang | Hao Chang https://creativecommons.org/licenses/by/4.0
Finite-time matrix projective synchronization of fractional-order memristor-based delayed neural networks with parameter uncertainty
This research examines the phenomenon of finite-time matrix projective synchronization (FTMPS) in the context of two distinct fractional-order memristor-based delayed neural networks (FOMDNNs). For the FOMDNNs with indeterminate parameters, some suitable controllers are structured, and sufficient conditions for implementing the FTMPS are demonstrated through some inequality techniques and relevant lemmas pertaining to fractional calculus. The synchronization issues under two different norm cases are fully considered. Subsequently, two numerical examples of the FTMPS are revealed and the discrepancies in their synchronization gradually tend to zero, which shows the validity and accuracy of the obtained synchronization results.
fractional-order memristive-based delayed neural networks
Copyright (c) 2026 Shangbin Xu | Bo Hu | Hai Zhang | Xinbin Chen | Jinde Cao https://creativecommons.org/licenses/by/4.0
Stability and stabilization for positive switched delay systems under mode-dependent interval dwell time
This paper explores the issues of exponential stability and positive stabilization of positive switched systems with time-varying delays. Using the Lyapunov–Razumikhin approach, we derive exponential stability criteria for positive switched delay systems (PSDSs) across various switching behaviors, including nondecreasing and decreasing switching patterns. Following this, we delve into the design of state feedback control to achieve positive stabilization of these systems, leveraging the established stability conditions. The paper culminates with numerical examples that confirm the validity of our theoretical findings.
Copyright (c) 2026 Xiukun Zhang | Yuangong Sun https://creativecommons.org/licenses/by/4.0
Adaptive event-triggered output-feedback stabilization for nonlinear systems with function control coefficients
This article presents an adaptive event-triggered control scheme for global stabilization of uncertain nonlinear systems with function control coefficients, input matching uncertainty, and unknown polynomial-function rates. A single dynamic gain observer is designed to handle these complexities, replacing the traditional dual-gain approach. An extended state observer asymptotically estimates the input matching uncertainty. An adaptive output-feedback controller, based on a time-varying threshold event-triggering mechanism, ensures closed-loop system stabilization and prevents Zeno behavior. Simulation results validate the proposed strategy
Copyright (c) 2026 Yu Zhang | Shaoli Jin | Hui Li | Yue Pan https://creativecommons.org/licenses/by/4.0
Observer-based distributed optimization for linear multiagent systems with external disturbances
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.
Copyright (c) 2026 Xuening Xu | Zhiyong Yu | Haijun Jiang https://creativecommons.org/licenses/by/4.0
Existence and stability results for triple systems of fractional Sturm–Liouville–Langevin equations with cyclic boundary conditions
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.
fractional Sturm–Liouville–Langevin equation
Copyright (c) 2026 Gang Chen | Zhanbing Bai | Wei Zhang https://creativecommons.org/licenses/by/4.0
Energetic formulation of the subgroup commutativity degree
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).
Copyright (c) 2026 Seid Kassaw Muhie | Daniele Ettore Otera | Francesco G. Russo https://creativecommons.org/licenses/by/4.0
Nonparametric changed segment detection in functional data
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.
Copyright (c) 2026 Karolis Bartkus | Alfredas Račkauskas https://creativecommons.org/licenses/by/4.0
Modeling the impact of detritus-based irrigation on agricultural crop production
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.
Copyright (c) 2026 Arvind Kumar Misra | Prinsi Shukla https://creativecommons.org/licenses/by/4.0