一类微生物絮凝模型平衡点的稳定性与Hopf分支

Stability and Hopf Bifurcation of a Class of Microbial Flocculation Model

考虑了一类具有营养循环的微生物絮凝常微分方程动力学模型.该类动力学模型平衡点可呈现前向与后向分支.利用常微分方程相关理论,研究了其边界平衡点的全局稳定性,以及正平衡点的局部稳定性析与Hopf分支存在性.同时,计算机数值模拟结果显示了与理论结果的一致性,并进一步揭示了该类动力系统可能呈现的复杂的振荡性质.

In this paper, we consider a class of ordinary differential equation dynamic model describing flocculation of microorganism and nutrient cycling. The equilibria of the dynamic model can behave forward and backward branches. Using the theory of ordinary differential equations, global stability of the boundary equilibrium, local stability of the positive equilibrium and the existence of Hopf bifurcation are analyzed.At the same time, the numerical simulation results are given.