Dynamics of a Delayed Prey-Predator System With Crowley-Martin Functional Response

Bryar Khdhir  Abas; Kawa Ahmad  Hassan

doi:10.24996/ijs.2024.65.9.27

Authors

Bryar Khdhir Abas Department of Mathematics, College of Science, University of Sulaimani, Sulaymaniah, Kurdistan, Kurdistan Region, Iraq https://orcid.org/0009-0009-0120-114X
Kawa Ahmad Hassan Department of Mathematics, College of Science, University of Sulaimani, Sulaymaniah, Kurdistan, Kurdistan Region, Iraq https://orcid.org/0000-0003-2114-7098

DOI:

https://doi.org/10.24996/ijs.2024.65.9.27

Keywords:

Prey-predator model, Crowley-Martin, Stability analysis, Hopf-bifurcation

Abstract

ln this paper, an ecological predator-prey model with time delay is proposed and studied analytically and numerically. The stability and bifurcation analysis of the proposed model with a Crowley-Martin response function are covered in this article. In the beginning, equilibrium points of the proposed model are identified. Secondly, the local asymptotic stability of the equilibria and Hopf-bifurcation are discussed by the characteristic equations of the system. Finally, by creating a suitable Lyapunov function and LaSalle’s invariance principle, the equilibria's global asymptotic stability is examined.