具Holling-Ⅳ功能反应项的分数阶捕食模型的定性分析及斑图动力学

Qualitative Analysis and Pattern Dynamics of the Fractional Predator-Prey Model with the Holling-Ⅳ Functional Response Term

斑图动力学是当代非线性分析领域的主要研究方向之一,非线性捕食-食饵模型的动力学行为成为其研究热点。主要研究了一类分数阶扩散的捕食系统:首先建立起系统的行波解的存在性并给出系统发生Hopf分岔的条件;其次利用分数阶微分方程的定性理论和Hopf分岔理论讨论了系统局部稳定、全局稳定以及图灵分岔发生的条件;最后利用Matlab软件进行数值模拟得到了系统的空间斑图。

Pattern dynamics is one of the main research directions in the field of contemporary nonlinear analysis,and the dynamic behavior of the nonlinear predator-prey model has become its research hotspot.This paper mainly studies a type of predator-prey system with fractional diffusion.Firstly,this paper establishes the existence of the traveling wave solutions of the system and gives the conditions of the Hopf bifurcation occurrence of the system.Then,it discusses the conditions of the local stability,global stability and Turing bifurcation occurrence of the system by using the qualitative theory of fractional differential equations and Hopf bifurcation theory.Finally,it uses Matlab software for numerical simulation and obtains the spatial pattern of the system.