Back to Search Start Over

Dynamics of a Class of Prey–Predator Models with Singular Perturbation and Distributed Delay.

Authors :
Gao, Jie
Zhang, Yue
Source :
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. Mar2024, Vol. 34 Issue 3, p1-16. 16p.
Publication Year :
2024

Abstract

In this paper, two prey–predator models with distributed delays are presented based on the growth and loss rates of the predator, which are much smaller than that of the prey, leading to a singular perturbation problem. It is obtained that Hopf bifurcation can occur, where the coexistence equilibrium becomes unstable leading to a stable limit cycle. Subsequently, considering the perturbation parameter 0 < ≪ 1 , the fact that the solution crossing the transcritical point converges to a stable equilibrium is discussed for the model with Holling type I using the linear chain criterion, center-manifold reduction, the geometric singular perturbation theory and entry–exit function. The existence and uniqueness of relaxation oscillation cycle for the model with Holling type II are obtained. In addition, numerical simulations are provided to verify the analytical results. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
02181274
Volume :
34
Issue :
3
Database :
Academic Search Index
Journal :
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
Publication Type :
Academic Journal
Accession number :
176408362
Full Text :
https://doi.org/10.1142/S0218127424500317