A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional response

Advances in Difference Equations

article

Savadogo, Assane¹  Sangaré, Boureima¹  Ouedraogo, Hamidou¹ 

[1] Department of Mathematics and Informatics

关键词: Prey-predator system;    Hopf-bifurcation;    Global stability;    Numerical simulations;   

DOI  :  10.1186/s13662-021-03437-2

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY