Dynamics of a diffusive predator–prey system with ratio-dependent functional response and time delay

Ran Zhang; Xin Jiang; Zhikun She

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Dynamics of a diffusive predator–prey system with ratio-dependent functional response and time delay

Dynamics of a diffusive predator–prey system with ratio-dependent functional response and time delay

作者：

Ran Zhang Xin Jiang Zhikun She

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Predator-prey

model

diffusive

time

delay

global

asymptotical

stability

Hopf

bifurcation

摘要：

In this paper,we investigate the qualitative behaviors of a predator–prey system with ratio-dependent function.The system accommodates the diffusion effect to model the migration of individuals and the time delay induced by reproduction.We start with some basic properties of the system.Then the sufficient condition independent of time delay and diffusion effect for global asymptotical stability of the boundary equilibrium is obtained by using the comparison principle.Afterwards,based on the LaSalle’s invariance principle and Lyapunov functional,we investigate the global attractiveness of the positive equilibrium,arriving at its global asymptotical stability.Further,Hopf bifurcation induced by time delay around the positive equilibrium is explored.Finally,numerical examples are listed to verify the corresponding analytical results.

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篇名	Dynamics of a diffusive predator–prey system with ratio-dependent functional response and time delay
来源期刊	生物数学学报:英文版	学科	数学
关键词	Predator-prey model diffusive time delay global asymptotical stability Hopf bifurcation
年，卷（期）	2020,（6）	所属期刊栏目
研究方向		页码范围	1-21
页数	21页	分类号	O17
字数		语种
DOI