一类具有猎物庇护和扩散的捕食-食饵系统的分岔分析

Chaoming Huang, Yiping Lin
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引用次数: 0

摘要

本文研究了一个包含恒定猎物庇护和扩散的延迟捕食者-猎物模型。通过分析与该模型相对应的线性化系统的特征方程,研究了系统正平衡点的局部渐近稳定性。Hopf分岔发生。利用范式和中心流形理论,导出了确定Hopf分岔方向和分岔周期解稳定性的显式算法。最后,通过数值模拟对分析结果进行了验证。随着时延的增加,系统出现混沌行为。
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Bifurcation Analysis for a Predator-Prey System with Prey Refuge and Diffusion
In this paper, a delayed predator-prey model incorporating a constant prey refuge and diffusion is studied. By analyzing the characteristic equation of linearized system corresponding to the model, we study the local asymptotic stability of the positive equilibrium of the system. Hopf bifurcation is occurred. By using the normal form and the center manifold theory, an explicit algorithm to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived. Finally, numerical simulations are performed to support the analytical results. With delay increasing, chaotic behaviors are observed.
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