具有Beddington-DeAngelis型功能反应的离散捕食者–食饵系统的动力学行为

Dynamical Behavior of Discrete Predator-Prey System with Beddington-Deangelis Functional Response

摘要: 在本文中，我们提出了一个离散的具有Beddington-DeAngelis型功能反应的捕食者–食饵系统。研究了该模型不动点的稳定性。同时，利用分支理论和近似流的方法，证明了离散模型经历了折分支和翻转分支。数值模拟不仅证明了我们的理论分析的一致性，而且还展示了复杂的动力学行为，如周期为2的倍周期分支级联和混沌集。数值计算了最大李雅普诺夫指数，进一步证实了动力学行为的复杂性。结果表明，离散模型比连续模型具有更丰富的动力学特性。

Abstract: In this paper, we propose a discrete Beddington-DeAngelis predator-prey system. The stability of the fixed points of this model is studied. At the same time, it is shown that the discrete model un-dergoes fold bifurcation and flips bifurcation by using bifurcation theory and the method of ap-proximation by a flow. Numerical simulation are presented not only to demonstrate the consistence with our theoretical analyses, but also to exhibit the complex dynamical behaviors, such as the cas-cade of period-doubling bifurcation in period-2 and the chaotic sets. The Maximum Lyapunov expo-nents are numerically computed to confirm further the complexity of the dynamical behaviors. These results show that the discrete model has more rich dynamic behaviors than the continuous model.