TITLE:
Dynamical Properties of a Discrete Lesley-Gower Prey-Predator Model with Holling-II Type Functional Response
AUTHORS:
Kaile Qiu, Wanying Li, Donghuan He, Guoqiang Qian, Xiaoliang Zhou
KEYWORDS:
Leslie-Gower Prey-Predator Model, Non-Hyperbolic Fixed Point, Flip Bifurcation, Neimark-Sacker Bifurcation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.11,
November
28,
2024
ABSTRACT: In this paper, we will study a class of discrete Leslie-Gower prey-predator models, which is a discretization of the continuous model proposed by Leslie and Gower in 1960. First, we find all fixed points, use hyperbolic and non-hyperbolic conditions to give the types of fixed points, and then analyze the bifurcation properties of non-hyperbolic fixed points. The generating conditions of Flip bifurcation and Neimark-Sacker bifurcation at fixed points are studied. Finally, numerical simulations of Flip bifurcation and Neimark-Sacker bifurcation are given.