一类酶促反应下的生化振荡模型中的Hopf分支

Hopf Bifurcation Analysis of a Class of Biochemical Oscillator Model of Enzymatic Reaction

借助规范型方法研究了酶促反应的非线性动力系统的Hopf分支的存在性,分支方向以及分支周期解的稳定性.研究表明酶浓度和反应物浓度满足一定关系时,系统出现周期震荡.k=1/8,λ=(3/8)～1/2时,系统出现退化Hopf分支.

In this paper, by means of Normal form theory, we study the nonlinear dynamic system of enzymatic reaction and analysis the existence of Hopf bifurcation, the direction of bifurcation and stability of bifurcating periodic solutions. Studies show that when the concentration of enzyme and reactants satisfies a certain relation, system appear periodic oscillation. When k=1/8,λ=（3/8）,system appear the degenerate Hopf bifurcation.