School of Mathematics and Physics, Wenzhou University, Wenzhou 325035, China.
Liushi No.3 Middle School, Wenzhou 325604, China.
Math Biosci Eng. 2021 Sep 10;18(6):7877-7918. doi: 10.3934/mbe.2021391.
In the paper, stability and bifurcation behaviors of the Bazykin's predator-prey ecosystem with Holling type Ⅱ functional response are studied theoretically and numerically. Mathematical theory works mainly give some critical threshold conditions to guarantee the existence and stability of all possible equilibrium points, and the occurrence of Hopf bifurcation and Bogdanov-Takens bifurcation. Numerical simulation works mainly display that the Bazykin's predator-prey ecosystem has complex dynamic behaviors, which also directly proves that the theoretical results are effective and feasible. Furthermore, it is easy to see from numerical simulation results that some key parameters can seriously affect the dynamic behavior evolution process of the Bazykin's predator-prey ecosystem. Moreover, limit cycle is proposed in view of the supercritical Hopf bifurcation. Finally, it is expected that these results will contribute to the dynamical behaviors of predator-prey ecosystem.
本文从理论和数值两方面研究了具有 Holling Ⅱ型功能反应的 Bazykin 捕食者-被捕食者生态系统的稳定性和分岔行为。数学理论工作主要给出了一些临界阈值条件，以保证所有可能平衡点的存在和稳定性，以及 Hopf 分岔和 Bogdanov-Takens 分岔的发生。数值模拟工作主要显示了 Bazykin 捕食者-被捕食者生态系统具有复杂的动态行为，这也直接证明了理论结果的有效性和可行性。此外，从数值模拟结果中可以很容易地看出，一些关键参数会严重影响 Bazykin 捕食者-被捕食者生态系统的动态行为演化过程。此外，针对超临界 Hopf 分岔提出了极限环。最后，期望这些结果将有助于捕食者-被捕食者生态系统的动力学行为。
