Ma Xiaomeng, Bai Zhanbing, Sun Sujing
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China.
Math Biosci Eng. 2023 Jan;20(1):437-455. doi: 10.3934/mbe.2023020. Epub 2022 Oct 10.
In this paper, a delayed fractional Lotka-Volterra food chain chemostat model with incommensurate orders is proposed, and the effect on system stability and bifurcation of this model are discussed. First, for the system with no controller, the stability and Hopf bifurcation with respect to time delay are investigated. Taking the time delay as the bifurcation parameter, the relevant characteristic equations are analyzed, and the conditions for Hopf bifurcation are proposed. The results show that the controller can fundamentally affect the stability of the system, and that they both have an important impact on the generation of bifurcation at the same time. Finally, numerical simulation is carried out to support the theoretical data.
本文提出了一个具有非等阶的时滞分数阶Lotka-Volterra食物链恒化器模型，并讨论了该模型对系统稳定性和分岔的影响。首先，对于无控制器的系统，研究了关于时滞的稳定性和Hopf分岔。以时滞为分岔参数，分析了相关特征方程，提出了Hopf分岔的条件。结果表明，控制器能从根本上影响系统的稳定性，并且它们同时对分岔的产生都有重要影响。最后，进行了数值模拟以支持理论数据。
