Double Hopf Bifurcation Analysis in the Memory-based Diffusion System

被引：19
作者：
Song, Yongli [1 ]
Peng, Yahong [2 ]
Zhang, Tonghua [3 ]
机构：
[1] Hangzhou Normal Univ, Sch Math, Hangzhou 311121, Peoples R China
[2] Donghua Univ, Dept Math, Shanghai 201620, Peoples R China
[3] Swinburne Univ Technol, Dept Math, Hawthorn, Vic 3122, Australia
来源：
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2024年 / 36卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Memory-based diffusion; Delay; Stability; Double Hopf bifurcation; Normal form; DELAYED CHEMOSTAT MODEL; FUNCTIONAL-DIFFERENTIAL EQUATIONS; GENERAL RESPONSE FUNCTIONS; BREAK-EVEN CONCENTRATION; ASYMPTOTIC-BEHAVIOR; NORMAL FORMS; SPATIOTEMPORAL DYNAMICS; MATHEMATICAL-MODEL; SPATIAL MOVEMENT; PERSISTENCE;
D O I：
10.1007/s10884-022-10180-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we derive the algorithm for calculating the normal form of the double Hopf bifurcation that appears in a memory-based diffusion system via taking memory-based diffusion coefficient and the memory delay as the perturbation parameters. Using the obtained theoretical results, we study the dynamical classification near the double Hopf bifurcation point in a predator-prey system with Holling type II functional response. We show the existence of different kinds of stable spatially inhomogeneous periodic solutions, the transition from one kind to the other as well as the coexistence of two types of periodic solutions with different spatial profiles by varying the memory-based diffusion coefficient and the memory delay.
引用
收藏
页码：1635 / 1676
页数：42
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