A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional response
Open Access
- 3 June 2021
- journal article
- research article
- Published by Springer Science and Business Media LLC in Advances in Difference Equations
- Vol. 2021 (1), 1-23
- https://doi.org/10.1186/s13662-021-03437-2
Abstract
In this paper, our aim is mathematical analysis and numerical simulation of a prey-predator model to describe the effect of predation between prey and predator with nonlinear functional response. First, we develop results concerning the boundedness, the existence and uniqueness of the solution. Furthermore, the Lyapunov principle and the Routh–Hurwitz criterion are applied to study respectively the local and global stability results. We also establish the Hopf-bifurcation to show the existence of a branch of nontrivial periodic solutions. Finally, numerical simulations have been accomplished to validate our analytical findings.Keywords
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