Flip bifurcation and Neimark-Sacker bifurcation in a discrete predator prey model with harvesting

• 作者: Wei Liu Yaolin Jiang
• 来源期刊: 生物数学学报:英文版
• 学科: 数学
• 关键词: Predator prey HARVESTING Flip bifurcation Neimark Sacker bifurcation chaos.
• 年，卷（期）: 2020,（1）
• 页码范围: 1-37
• 页数: 37页
• 分类号: O17

摘要

In this paper,a difference-algebraic predator prey model is proposed,and its complex dynamical behaviors are analyzed.The model is a discrete singular system,which is obtained by using Euler scheme to discretize a differential-algebraic predator-prey model with harvesting that we establish.Firstly,the local stability of the interior equilibrium point of proposed model is investigated on the basis of discrete dynamical system the­ory.Further,by applying the new normal form of difference-algebraic equations,center manifold theory and bifurcation theory,the Flip bifurcation and Neimark-Sacker bifur­cation around the interior equilibrium point are studied,where the step size is treated as the variable bifurcation parameter.Lastly,with the help of Matlab software,some numerical simulations are performed not only to validate our theoretical results,but also to show the abundant dynamical behaviors,such as period-doubling bifurcations,period 2,4,8,and 16 orbits,invariant closed curve,and chaotic sets.In particular,the corresponding maximum Lyapunov exponents are numerically calculated to corroborate the bifurcation and chaotic behaviors.