Bifurcation analysis and chaos control in discrete-time modified Leslie–Gower prey harvesting model

Advances in Difference Equations

article

Bilal Ajaz, Muhammad¹  Saeed, Umer²  Din, Qamar³  Ali, Irfan¹  Israr Siddiqui, Muhammad² 

[1] School of Natural Sciences, National University of Sciences and Technology;NUST Institute of Civil Engineering, School of Civil and Environmental Engineering, National University of Sciences and Technology;Department of Mathematics, University of Poonch Rawalakot

关键词: Modified Leslie–Gower model;    Stability analysis;    Period-doubling bifurcation;    Neimark–Sacker bifurcation;    Chaos control;   

DOI  :  10.1186/s13662-020-2498-1

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

We investigate the dynamical behavior of a modified Leslie–Gower prey–predator model with harvesting in prey population. In order to explore rich dynamics of the model, Euler approximation is implemented to obtain a discrete-time modified Leslie–Gower model. Existence of equilibria and their local asymptotic stabilities are carried out. Furthermore, with the help of bifurcation theory and center manifold theorem, existence and directions of period-doubling and Neimark–Sacker bifurcations are investigated at positive steady-state. In order to control chaos and bifurcations, the Ott–Grebogi–Yorke (OGY) method and the hybrid control strategy are introduced. Numerical simulations are also provided to illustrate the theoretical discussions.

【 授权许可】

CC BY