Stability and Hopf Bifurcation in the General Langford System

被引：0
作者：
Gaihui Guo
Jingjing Wang
Meihua Wei
机构：
[1] Shaanxi University of Science and Technology,School of Mathematics and Data Science
来源：
Qualitative Theory of Dynamical Systems | 2023年 / 22卷
关键词：
General Langford system; Hopf bifurcation; Diffusion; Stability; 35K57; 35B32; 35B35;
D O I：
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学科分类号：
摘要：
This paper is concerned with the general Langford system under homogeneous Neumann boundary conditions. The stabilities of constant solutions are discussed for the general Langford ODE and PDE systems, respectively. Based on the stability results, for the Langford ODE system, the existence, bifurcation direction and stability of periodic solutions are established. Then for the Langford PDE system, by the center manifold theory and the normal form method, the direction of Hopf bifurcation and the stability of spatially homogeneous periodic solutions are investigated. Finally, numerical simulations are shown to support and supplement the results of theoretical analysis.
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