Dynamics in a delayed diffusive cell cycle model
Articles
Yanqin Wang
Soochow University; Changzhou University
Ling Yang
Soochow University, China
Jie Yan
Soochow University, China
Published 2018-10-22
https://doi.org/10.15388/NA.2018.5.4
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Keywords

cell cycle model
delay
diffusion
Hopf bifurcation
stability

How to Cite

Wang, Y., Yang, L. and Yan, J. (2018) “Dynamics in a delayed diffusive cell cycle model”, Nonlinear Analysis: Modelling and Control, 23(5), pp. 691–709. doi:10.15388/NA.2018.5.4.

Abstract

In this paper, we construct a delayed diffusive model to explore the spatial dynamics of cell cycle in G2/M transition. We first obtain the local stability of the unique positive equilibrium for this model, which is irrelevant to the diffusion. Then, through investigating the delay-induced Hopf bifurcation in this model, we establish the existence of spatially homogeneous and inhomogeneous bifurcating periodic solutions. Applying the normal form and center manifold theorem of functional partial differential equations, we also determine the stability and direction of these bifurcating periodic solutions. Finally, numerical simulations are presented to validate our theoretical results.

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