论文标题
带有II型功能响应的三种物种食物链模型的动力学
Dynamics of Three Species Food Chain Model with Holling type II Functional Response
论文作者
论文摘要
在这项工作中，我们以不同的观点重新审视了经典的II型三物种食物链模型。两个关键参数$λ_1$和$λ_2$定义了其他六个参数。我们表明，所有平衡的局部稳定性和存在可以由$λ_1$和$λ_2$重新校正，并且给出了参数及其相应动态的完整分类。通过分析原理显示了三个全局灭绝结果。此外，在数值上介绍了一些有趣的数值模拟，包括混乱现象，双稳定性现象，包括平衡周期双稳定性和循环周期双稳定性。最后，给出了简短的讨论和生物学意义。
In this work, we revisit the classical Holling type II three species food chain model with a different viewpoint. Two critical parameters $λ_1$ and $λ_2$ dependent on other six parameters are defined. We show that local stabilities and existence of all equilibria can be reformulated by $λ_1$ and $λ_2$, and the complete classifications of parameters and its corresponding dynamics are given. Three global extinction results are showed by comparison principle analytically. Moreover, some interesting numerical simulations, including the chaotic phenomena, and the bi-stability phenomena, including equilibrium-cycle bi-stability and cycle-cycle bi-stability, are presented numerically. Finally, a brief discussion and biological implications are given.
