Turing instability and Hopf bifurcation for a diffusion-plankton system with cell size

被引:5
|
作者
Zhao Qiuyue [1 ]
Liu Shutang [1 ]
Niu Xinglong [2 ]
机构
[1] Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Peoples R China
[2] North Univ China, Sch Elect & Control Engn, Taiyuan, Peoples R China
基金
中国国家自然科学基金;
关键词
Diffusive plankton system; Turing instability; Hopf bifurcation; cell size; time delay; PHYTOPLANKTON-ZOOPLANKTON MODEL; SPATIOTEMPORAL DYNAMICS; NPZ MODEL; DELAY; GROWTH;
D O I
10.1080/00207160.2020.1755433
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper investigates Turing instability and Hopf bifurcation for a diffusive plankton system with time delay and cell size. To determine the effects of diffusion and cell size on the dynamics of the system, we first study the system without time delay, where the conditions of stability of coexisting equilibrium and Turing instability are obtained through Routh-Hurwitz criterion. Then we give the existence of Hopf bifurcation using time delay as bifurcation parameter by analyzing the distribution of eigenvalues, and derive the property of Hopf bifurcation by applying the centre manifold theory. Finally, numerical simulation shows that different cell size increases the variety of dynamics for diffusive plankton system.
引用
收藏
页码:480 / 501
页数:22
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