CODIMENSION-TWO BIFURCATIONS OF A TWO-DIMENSIONAL DISCRETE TIME LOTKA-VOLTERRA PREDATOR-PREY MODEL

被引：3
|
作者：
Ma, Jiying [1 ]
Duan, Mingxia [1 ]
机构：
[1] Univ Shanghai Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2024年 / 29卷 / 03期
关键词：
Discrete predator-prey model; codimension-two bifurcations; 1; 2; res-onance; 3; resonance; 4; POPULATIONS; DYNAMICS; SYSTEM; CHAOS;
D O I：
10.3934/dcdsb.2023131
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the codimension-two bifurcations of a two-dimensional discrete time predator-prey model, which is derived from a classical Lotka-Volterra type predator-prey system by the forward Euler scheme. It is shown that the model undergoes codimension-two bifurcations associated with 1:2, 1:3 and 1:4 resonances. The conditions for strong res-onance bifurcations are obtained by using the normal form method and the theory of approximation by a flow. Moreover, the bifurcation curves around 1:2 resonance are obtained and returned to the original parameters. Numerical simulations are provided to illustrate our theoretical results, and the model exhibits complex dynamical behaviors such as quasi-periodic orbits and the chaotic sets.
引用
收藏
页码：1217 / 1242
页数：26
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