Year: 2024
Author: Xiaohui Chen, Wensheng Yang
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 4 : pp. 1064–1082
Abstract
In this paper, we consider a Leslie-Gower predator-prey model with a square root functional response while prey forms a herd as a form of group defense. We show that the solution of the system is non-negative and bounded. By applying the blow-up technique, it can be deduced that the origin displays instability. Moreover, employing the proof-by-contradiction approach, we demonstrate that the unique equilibrium point can be globally asymptotically stable under certain conditions. The sufficient conditions for the occurrence, stability, and direction of Hopf bifurcation are obtained. We further explore the conditions for the existence and uniqueness of the limit cycle. Theoretical results are validated through numerical simulations. Thus, our findings reveal that herd behavior has an important impact on the Leslie-Gower prey-predator system.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2024.1064
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 4 : pp. 1064–1082
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Leslie-Gower predator-prey model herd behavior stability Hopf bifurcation limit cycle.