Bifurcation analysis of a diffusive predator–prey model with ratio-dependent Holling type III functional response
Bifurcation analysis of a diffusive predator–prey model with ratio-dependent Holling type III functional response
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DOI：
10.1007/s11071-015-2088-z
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发表时间：
2015-04
影响因子：
5.6
通讯作者：
Jun Zhou
中科院分区：
文献类型：
--
作者：
Jun Zhou
本文研究了在均匀诺依曼边界条件下具有比率依赖性霍林 III 型功能响应的反应扩散捕食者-被捕食系统的空间、时间和时空动力学。对基于常微分方程的空间齐次模型的局部渐近稳定性和Hopf分岔进行了初步分析。对于反应扩散模型，首先讨论了唯一恒定稳态的稳定或不稳定的参数区域。然后表明出现图灵（扩散驱动）不稳定性，从而导致空间不均匀模式。接下来，证明该模型表现出 Hopf 分岔，从而产生时间不均匀模式。最后，分别用分岔法和能量法建立了非常数稳态解的存在性和不存在性。提出了数值模拟来验证和说明理论结果。
The spatial, temporal, and spatiotemporal dynamics of a reaction–diffusion predator–prey system with ratio-dependent Holling type III functional response, under homogeneous Neumann boundary conditions, are studied in this paper. Preliminary analysis on the local asymptotic stability and Hopf bifurcation of the spatially homogeneous model based on ordinary differential equation is presented. For the reaction–diffusion model, firstly the parameter regions for the stability or instability of the unique constant steady state are discussed. Then it is shown that Turing (diffusion-driven) instability occurs, which induces spatial inhomogeneous patterns. Next, it is proved that the model exhibits Hopf bifurcation, which produces temporal inhomogeneous patterns. Finally, the existence and nonexistence of nonconstant steady- state solutions are established by bifurcation method and energy method, respectively. Numerical simulations are presented to verify and illustrate the theoretical results.