A study of stability and bifurcation analysis in discrete-time predator—prey system involving the Allee effect

Seval Isik

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A study of stability and bifurcation analysis in discrete-time predator—prey system involving the Allee effect

A study of stability and bifurcation analysis in discrete-time predator—prey system involving the Allee effect

作者：

Seval Isik

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PREDATOR-PREY

SYSTEM

fixed

point

stability

Neimark-Sacker

BIFURCATION

Allee

effect

摘要：

This paper deals with a discrete-time predator-prey system which is subject to an Allee effect on prey.We investigate the existence and uniqueness and find parametric conditions for local asymptotic stability of fixed points of the discrete dynamic system.Moreover,using bifurcation theory,it is shown that the system undergoes Neimark-Sacker bifurcation in a small neighborhood of the unique positive fixed point and an inv aria nt circle will appear.Then the direction of bifurcation is given.Furthermore,numerical analysis is provided to illustrate the theoretical discussions with the help of Matlab packages.Thus,the main theoretical results are supported with numerical simulations.

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篇名	A study of stability and bifurcation analysis in discrete-time predator—prey system involving the Allee effect
来源期刊	生物数学学报:英文版	学科	社会科学
关键词	PREDATOR-PREY SYSTEM fixed point stability Neimark-Sacker BIFURCATION Allee effect
年，卷（期）	2019,（1）	所属期刊栏目
研究方向		页码范围	255-269
页数	15页	分类号	G
字数		语种
DOI