Period-doubling Bifurcation and Stability in a Two Dimensional Discrete Prey-predator Model with Allee Effect and Immigration Parameter on Prey

npj Clean Water

article

Figen KANGALGİL¹  Feda İLHAN² 

[1] Dokuz Eylül University Bergama Vocational School;BOLU ABANT IZZET BAYSAL UNIVERSITY

关键词: Prey-predator model;    Stability analysis;    Fixed point;    Allee effect;    Period-doubling bifurcation;   

DOI  :  10.17776/csj.1026330

学科分类：社会科学、人文和艺术（综合）

来源: Springer

【 摘 要 】

This article is about the dynamics of a discrete-time prey-predator system with Allee effect and immigrationparameter on prey population. Particularly, we study existence and local asymptotic stability of the uniquepositive fixed point. Furthermore, the conditions for the existence of bifurcation in the system are derived. Inaddition, it is shown that the system goes through period-doubling bifurcation by using bifurcation theory andcenter manifold theorem. Eventually, numerical examples are given to illustrate theoretical results.

【 授权许可】

CC BY