Bifurcation and chaos in a discrete-time predator-prey system with strong Allee effect

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2026-07-01 Epub Date: 2026-01-27 DOI:10.1016/j.cnsns.2026.109794

Kunlun Huang , Xintian Jia , Yanqi Zhang , Ya Li , Cuiping Li

引用次数: 0

Abstract

A discrete-time system incorporating a strong Allee effect, derived by discretizing the corresponding continuous predator-prey model via the Euler method, is analyzed. Stability analysis reveals that when the predator mortality rate exceeds a critical threshold, two interior equilibria emerge, enabling coexistence of both species. Bifurcation analysis further demonstrates that the system may undergo flip and Neimark-Sacker bifurcations in response to parameter variations. The findings indicate that a strong Allee effect stabilizes the system by generating stable equilibrium points, whereas a weak Allee effect can induce more complex dynamics, such as periodic orbits and chaotic attractors. Additionally, the results highlight the system’s high sensitivity to ecological parameters, including predator population growth rate and environmental protection measures.

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具有强Allee效应的离散捕食-食饵系统的分岔与混沌

通过欧拉方法离散相应的连续捕食者-猎物模型，得到了一个具有强Allee效应的离散时间系统。稳定性分析表明，当捕食者死亡率超过临界阈值时，出现两个内部平衡，使两个物种能够共存。分岔分析进一步证明了系统在参数变化时可能发生翻转分岔和neimmark - sacker分岔。研究结果表明，强Allee效应通过产生稳定的平衡点来稳定系统，而弱Allee效应会引起更复杂的动力学，如周期轨道和混沌吸引子。此外，研究结果还显示了该系统对捕食者种群增长率和环境保护措施等生态参数的高度敏感性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.