一类时滞自催化可逆生化反应模型的Hopf分支及其稳定性

Hopf bifurcation and stability for an autocatalytic reversible biochemical reaction model with time delay

基于Hopf分支理论,研究一类具有时滞效应的自催化三分子可逆生化反应模型.以时滞τ为参数,建立正常数平衡点的稳定性和Hopf分支的存在性.利用中心流形定理和规范型理论,给出Hopf的分支方向和稳定性判定条件.借助数值模拟,验证理论分析结果.

Based on the Hopf bifurcation theory,an autocatalytic three-molecular reversible biochemical reaction model with time delay is considered.First,the stability of the equilibrium and the existence of Hopf bifurcation are obtained by choosing the delayτas parameter.Secondly,the direction and stability of Hopf bifurcation are determined by the normal form theory and the center manifold theorem.Finally,some numerical simulations are presented to verify the theoretical results.