Hopf Bifurcation in a Predator–Prey System with Infection

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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.

作者简介

A. Krishchenko

Bauman Moscow State Technical University, Moscow, 105005, Russia; Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333, Russia

Email: apkri@bmstu.ru
Москва Россия

O. Podderegin

Bauman Moscow State Technical University, Moscow, 105005, Russia

编辑信件的主要联系方式.
Email: podderegino@gmail.com
Москва Россия

参考

  1. Bate A.M., Hilkerr F.M. Complex dynamics in an eco-epidemiological model // Bull. Math. Biol. 2013. V. 75. P. 2059-2078.
  2. Крищенко А.П. Локализация инвариантных компактов динамических систем // Дифференц. уравнения. 2005. Т. 41. № 12. С. 1597-1604.
  3. Арнольд В.И. Обыкновенные дифференциальные уравнения. М., 2012.

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