一类具有时滞的Lengel-Epstein系统的稳定性分析

Study on Asymptotic Stability of Lengel-Epstein Model with Time Delay

在化学反应中,反应物自身分解一般会对反应物的浓度变化产生影响,而反应物自身分解需要的时间不可忽略,从而对反应物浓度变化的影响存在一定的时间滞后性。本文考虑了Lengel-Epstein模型中带有时滞微分方程组,利用线性化和分析相应特征方程的方法,对模型中正平衡点的局部渐近稳定性进行分析,并讨论了Hopf分支是否存在。

In chemical reactions,the concentration of the reactants may be affected by the decomposition of reactants,as there is always a delay in the concentration change,the time required for the decomposition cannot be ignored.Considering the differential equations with time delay in Lengel-Epstein model,this paper used linearization method and analysis of the corresponding characteristic equations to investigate the local asymptotic stability of the positive equilibrium point in the model.And the existence of Hopf branch was also discussed.