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具有Allee效应和恐惧效应的捕食–食饵系统动力学性质
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Abstract:
本文研究一类具有Allee效应和恐惧效应的捕食–食饵模型。我们讨论系统平衡点的存在性，接着分析边界平衡点和正平衡点的稳定性。同时证明系统存在鞍结分支。当Allee效应越强时，越不利于食饵和捕食者种群生存。通过数值模拟，验证系统存在极限环，同时出现双稳现象。增大恐惧效应，会使得正平衡点从不稳定变成稳定，也就是较大的恐惧效应可以促进系统的稳定。
This paper studies a predator-prey system with Allee effect and fear effect. We discuss the existence of the equilibria in the system, and analyze the stability of the boundary equilibria and positive equilibria. Also we prove that the system has a saddle-node bifurcation. When the Allee effect is large, it is unfavorable to the survival of prey and predator populations. Through numerical simulation, it is verified that the system has a limit cycle, and show the bistable phenomenon. Increasing the fear effect will make the positive equilibrium from unstable to stable, that is, a larger fear effect can promote the stability of the system.
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