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Transition to Diffusion Chaos in a Model of a “Predator–Prey” System with a Lower Threshold for the Prey Population
Differential Equations ( IF 0.6 ) Pub Date : 2020-05-01 , DOI: 10.1134/s0012266120050122
T. V. Karamysheva , N. A. Magnitskii

Abstract We carry out an analytical and numerical analysis of a model of the “predator–prey” system with a lower prey population threshold. The model is described by a system of partial differential equations of the “reaction–diffusion” type. Conditions are found for the bifurcation of periodic spatially homogeneous and spatially inhomogeneous solutions from the system thermodynamic branch. It is shown that transition to diffusion chaos in the model occurs in full agreement with the universal Feigenbaum–Sharkovskii–Magnitskii bifurcation theory via a subharmonic cascade of bifurcations of stable limit cycles.

中文翻译:

在具有较低猎物种群阈值的“捕食者-猎物”系统模型中过渡到扩散混沌

摘要 我们对具有较低猎物种群阈值的“捕食者-猎物”系统模型进行了解析和数值分析。该模型由“反应-扩散”类型的偏微分方程系统描述。从系统热力学分支找到周期性空间齐次和空间非齐次解的分叉条件。结果表明,模型中向扩散混沌的转变与通用 Feigenbaum-Sharkovskii-Magnitskii 分岔理论完全一致,通过稳定极限环分岔的次谐波级联。
更新日期:2020-05-01
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