一类具有互补型营养基的时滞恒化器模型Hopf分支的存在性

Existence of Hopf Bifurcation for a Delay Chemostat Model with Complementary Nutrients

该文研究了一类具有互补型营养基和两个不同时滞的微生物培养恒化器模型.首先利用Lyapunov函数和极限集理论使系统降维,然后对时滞分情况讨论其对系统动力学行为的影响,得到系统平衡点稳定和Hopf分支存在的充分条件.最后,通过数值模拟验证了主要结论的正确性.

This paper studies the existence of Hopf bifurcation for a chemostat model with complementary nutrients and two different delays.Firstly,a four dimension system is reduced to a two dimension system by Lyapunov function and limit set theory.Afterwards,according to the different cases of the delays,respectively,the influence of delays on the dynamic behaviors of the system is discussed,the sufficient conditions are obtained for the stability of the positive equilibrium and the existence of Hopf bifurcation in this system.Finally,some numerical simulations are carried out to verify the theoretical results in this paper.