Hopf bifurcation and chaos in a Leslie–Gower prey–predator model with discrete delays

• 作者: Anuraj Singh Pradeep Malik Preeti
• 来源期刊: 生物数学学报:英文版
• 学科: 数学
• 关键词: Discrete delays limit cycle global stability Hopf bifurcation chaotic behavior
• 年，卷（期）: 2020,（6）
• 页码范围: 135-161
• 页数: 27页
• 分类号: O17

摘要

In this work,a Leslie–Gower prey-predator model with two discrete delays has been investigated.The positivity,boundedness and persistence of the delayed system have been discussed.The system exhibits the phenomenon of Hopf bifurcation with respect to both delays.The conditions for occurrence of Hopf bifurcation are obtained for different combinations of delays.It is shown that delay induces the complexity in the system and brings the periodic oscillations,quasi-periodic oscillations and chaos.The properties of periodic solution have been determined using central manifold and normal form theory.Further,the global stability of the system has been established for different cases of discrete delays.The numerical computation has also been performed to verify analytical results.