有感染的捕食者-猎物系统中的霍普夫分岔

Pub Date : 2023-12-29 DOI:10.1134/s00122661230110125

A. P. Krishchenko, O. A. Podderegin

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引用次数: 0

摘要

摘要我们以一个三维常微分方程系统的形式研究了一个捕食者--猎物系统模型，其中猎物可能受到感染。利用紧凑不变集的定位方法，证明了吸引子的存在，并找到了估计其位置的紧凑正不变集。找到了种群灭绝和均衡存在的条件。提出了寻找非平衡的霍普夫分岔的数值方法，并给出了一个产生稳定极限循环的例子。

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Hopf Bifurcation in a Predator–Prey System with Infection

Abstract

We study a model of a predator–prey system with possible infection of prey in the form of a three-dimensional system of ordinary differential equations. Using the localization method of compact invariant sets, the existence of an attractor is proved and a compact positively invariant set is found that estimates its position. The conditions for the extinction of populations and the existence of equilibria are found. A numerical method for finding a Hopf bifurcation of the inner equilibrium is proposed and an example of an arising stable limit cycle is given.

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