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RAS MathematicsДифференциальные уравнения Differential Equations

  • ISSN (Print) 0374-0641
  • ISSN (Online) 3034-5030

Hopf Bifurcation in a Predator–Prey System with Infection

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PII
10.31857/S0374064123110122-1
DOI
10.31857/S0374064123110122
Publication type
Article
Status
Published
Authors
A. P. Krishchenko
  • Affiliation:
    Bauman Moscow State Technical University, Moscow, 105005, Russia
    Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333, Russia
O. A. Podderegin
  • Affiliation: Bauman Moscow State Technical University, Moscow, 105005, Russia
Volume/ Edition
Volume 59 / Issue number 11
Pages
1566-1570
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.
Keywords
Date of publication
19.09.2025
Year of publication
2025
Number of purchasers
0
Views
7

References

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