Dynamical analysis of a delayed predator-prey system with modified Leslie-Gower and Beddington-DeAngelis functional response

Advances in Difference Equations

Juan Liu¹ 

[1] Department of Mathematics and Physics, Bengbu College, Bengbu, P.R. China

关键词: delays;    Hopf bifurcation;    predator-prey system;    stability;    periodic solution;   

DOI  :  10.1186/1687-1847-2014-314

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The dynamics of a delayed predator-prey system with modified Leslie-Gower and Beddington-DeAngelis functional response is investigated. The main results are given in terms of local stability and local Hopf bifurcation. By regarding the possible combination of the feedback delays of the prey and the predator as a bifurcation parameter, sufficient conditions for the local stability and existence of the local Hopf bifurcation of the system are obtained. In particular, the properties of the local Hopf bifurcation such as direction and stability are determined by using the normal form method and center manifold theorem. Finally, numerical simulations are carried out to illustrate the main theoretical results.

【 授权许可】

CC BY