Hopf Bifurcation and Chaos Analysis of a Microbial Continuous Culture Model with Time Delay
Hopf Bifurcation and Chaos Analysis of a Microbial Continuous Culture Model with Time Delay
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DOI：
10.1515/ijnsns.2006.7.3.305
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发表时间：
2006
影响因子：
1.5
通讯作者：
Y.‐F. Ma;Z. Xiu;L. Sun;E. Feng
中科院分区：
文献类型：
--
作者：
Y.‐F. Ma;Z. Xiu;L. Sun;E. Feng
将底物和产物的离散时滞引入到微生物细胞的比生长速率中，并在此基础上建立了同时考虑底物和产物的代谢溢出和抑制作用的动力学模型。本文研究了时滞对平衡点稳定性的影响和模型的动力学行为。模型分析表明，当时滞超过其临界值时，平衡点的稳定性会发生变化。当时滞作为分岔参数时，系统发生Hopf分岔.由Hopf分支产生的周期解的稳定性是可变的，当时滞超过一定值时，会产生新的周期解，最终导致混沌的发生。
A discrete time delay for substrate and product is introduced into specific growth rate of microbial cells, on which the kinetic model is proposed by incorporating both metabolic overflow and inhibitions of substrate and product. The effect of delay on stability of equilibria and dynamic behavior of the model are studied in this paper. Model analysis shows that the stability of equilibrium can be changed as the time delay exceeds its critical value. Hopf bifurcation occurs if the time delay is taken as a bifurcation parameter. The stability of periodic solutions emanating from Hopf bifurcation is changeable and new periodic solutions occur when the time delay exceeds a certain value, which finally leads to occurrence of chaos.