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

页码：1217 / 1242

页数：26

共 50 条

[1] Bifurcations in a discrete time Lotka-Volterra predator-prey system
Liu, Xiaoli
Xiao, Dongmei
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2006, 6 (03): : 559 - 572
[2] Bifurcations and Marotto's chaos of a discrete Lotka-Volterra predator-prey model
Li, Yanan
Liu, Lingling
Chen, Yujiang
Yu, Zhiheng
PHYSICA D-NONLINEAR PHENOMENA, 2025, 472
[3] Bifurcations of a two-dimensional discrete-time predator-prey model
Khan, Abdul Qadeer
ADVANCES IN DIFFERENCE EQUATIONS, 2019, 2019 (1)
[4] CODIMENSION-ONE AND CODIMENSION-TWO BIFURCATIONS OF A DISCRETE LESLIE-GOWER TYPE PREDATOR-PREY MODEL
Long, Yuhua
Pang, Xiaofeng
Zhang, Qinqin
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2025, 30 (04): : 1357 - 1389
[5] Codimension-one and codimension-two bifurcations of a discrete predator-prey system with strong Allee effect
Zhang, Limin
Zhang, Chaofeng
He, Zhirong
MATHEMATICS AND COMPUTERS IN SIMULATION, 2019, 162 : 155 - 178
[6] Global Dynamics and Bifurcations Analysis of a Two-Dimensional Discrete-Time Lotka-Volterra Model
Khan, A. Q.
Qureshi, M. N.
COMPLEXITY, 2018,
[7] Codimension one and codimension two bifurcations in a discrete Kolmogorov type predator-prey model
Yousef, A. M.
Algelany, Ahmed M.
Elsadany, A. A.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2023, 428
[8] Periodic solutions of a discrete nonautonomous Lotka-Volterra predator-prey model with time delays
Xu, R
Chaplain, MAJ
Davidson, FA
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2004, 4 (03): : 823 - 831
[9] Bifurcations of a two-dimensional discrete-time predator–prey model
Abdul Qadeer Khan
Advances in Difference Equations, 2019
[10] Codimension-Two Bifurcation in a Class of a Discrete-Time Predator-Prey Interaction with Cannibalism
Khan, Muhammad Asif
Din, Qamar
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2025, 24 (02)

← 1 2 3 4 5 →