Hopf Bifurcations in a Predator-Prey System of Population Allelopathy with Discrete Delay

• 作者: Haihong Liu Xinhui Wang
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: LOTKA-VOLTERRA PREDATOR-PREY System Discrete Delay ALLELOPATHY Stability HOPF BIFURCATION Periodic Solution
• 年，卷（期）: yysxyw_2012,（6）
• 页码范围: 652-661
• 页数: 10页
• 分类号: O1

摘要

A delayed Lotka-Volterra two-species predator-prey system of population allelopathy with discrete delay is considered. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium is investigated and Hopf bifurcations are demonstrated. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations (FDEs). Finally, some numerical simulations are carried out for illustrating the theoretical results.