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Hopf Bifurcation in a Predator–Prey System with Infection
- Authors: Krishchenko A.P.1,2, Podderegin O.A.1
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Affiliations:
- Bauman Moscow State Technical University, Moscow, 105005, Russia
- Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333, Russia
- Issue: Vol 59, No 11 (2023)
- Pages: 1566-1570
- Section: Articles
- URL: https://rjmseer.com/0374-0641/article/view/649457
- DOI: https://doi.org/10.31857/S0374064123110122
- EDN: https://elibrary.ru/PEXCDU
- ID: 649457
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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.
About the authors
A. P. 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. A. Podderegin
Bauman Moscow State Technical University, Moscow, 105005, Russia
Author for correspondence.
Email: podderegino@gmail.com
Москва Россия
References
- Bate A.M., Hilkerr F.M. Complex dynamics in an eco-epidemiological model // Bull. Math. Biol. 2013. V. 75. P. 2059-2078.
- Крищенко А.П. Локализация инвариантных компактов динамических систем // Дифференц. уравнения. 2005. Т. 41. № 12. С. 1597-1604.
- Арнольд В.И. Обыкновенные дифференциальные уравнения. М., 2012.
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