具有时滞的基因表达模型的稳定性与分支分析

Stability and Bifurcation Analysis of a Gene Expression Model with Time Delay

应用频域法研究了一类具有三个时滞的基因表达模型的Hopf分支问题.基于Nyquist稳定性准则和Hopf分支定理,选取三个时滞的和τ作为分支参数,发现当τ超过某个临界值时,系统产生了Hopf分支.最后,对系统进行了数值仿真,数值仿真的结果验证了理论分析的正确性.

In this paper,Hopf bifurcation of a class of gene expression model with three time delays is studied by using frequency domain approach.Based on Nyquist stability criterion and the Hopf bifurcation theorem,τ,i.e.,the sum of the three delays ,is chosen as the bifurcation parameter and it is demonstrated that the Hopf bifurcation would occur when τ exceeds a critical value.Numerical simulation for justifying the theoretical results is also provided.