基于时滞反馈的一类基因表达模型的分岔控制

Hopf Bifurcation Control for a Gene Expression Model Via Delayed Feedback

针对一类具时滞的基因表达模型的Hopf分岔控制问题,提出一种基于时滞反馈的分岔控制方法.以时滞为分岔参数,指出无控制的系统当时滞增加到一定数值时,稳定性遭到破坏,使Hopf分岔过早产生.引入时滞反馈控制器可以延迟有害Hopf分岔的发生或使Hopf分岔消失,最后通过数值模拟验证了该理论的正确性.

In this paper,a time-delayed feedback controller is applied to a gene expression model with time delay in order to control Hopf bifurcation.By choosing time delay as a bifurcation parameter,it has been shown that the system without control cannot guarantee a stationary state and a Hopf bifurcation occurs when the bifurcation parameter passes through a critical value.Therefore,a control approach based on time-delayed feedback is proposed to postpone the onset of undesired Hopf bifurcation.Some numerical simulations for justifying the theoretical analysis are also provided.