DOUBLE HOPF BIFURCATION IN NONLOCAL REACTION-DIFFUSION SYSTEMS WITH SPATIAL AVERAGE KERNEL

被引：6

作者：

Shen, Z. U. O. L. I. N. ^{[1
]}

Liu, Y. A. N. G. ^{[1
]}

Wei, J. U. N. J. I. E. ^{[2
]}

机构：

[1] Harbin Univ Sci & Technol, Dept Basic Educ, Weihai 264300, Shandong, Peoples R China

[2] Harbin Inst Technol, Dept Math, Weihai 264209, Shandong, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2022年

基金：

中国国家自然科学基金;

关键词：

  Reaction-diffusion system; double Hopf bifurcation; nonlocal effect; normal forms; FUNCTIONAL-DIFFERENTIAL EQUATIONS; VOLTERRA TYPE SYSTEM; FISHER-KPP EQUATION; SPATIOTEMPORAL DYNAMICS; NORMAL FORMS; WAVE-FRONTS; PATTERN-FORMATION; GLOBAL STABILITY; POPULATION-MODEL; TRAVELING-WAVES;

D O I：

10.3934/dcdsb.2022176

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a general reaction-diffusion system with nonlocal effects and Neumann boundary conditions, where a spatial average kernel is chosen to be the nonlocal kernel. By virtue of the center manifold reduction technique and normal form theory, we present a new algorithm for computing normal forms associated with the codimension-two double Hopf bifurcation. The theoretical results are applied to a predator-prey model, and complex dynamic behaviors such as spatially nonhomogeneous periodic oscillations and spatially nonhomogeneous quasi-periodic oscillations could occur.

引用

页码：2424 / 2462

页数：39

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