有抑制时Gierer-Meinhardt模型的数值分支分析

Numerical Bifurcation Analysis of Gierer-Meinhardt's Model With Inhibition

对有抑制时的Gierer-Meinhardt模型 ,数学分析只给出了极限环存在的充分条件。应用Hopf分支理论 ,对有抑制时的Gierer -Meinhardt模型进行了数值分支分析 ,分析表明 ,当以k为分支参数时 ,p =a +b-2ac/[x (1 +kx2 ) ]≤ 0是极限环存在的阀值条件 ,该临界点为Hopf分支点。随着k的增大 。

Only an sufficient condition on existence of limit cycles has been obtained by mathematical analysis for the Gierer - Meinhardt's model with inhibition. By taking the inhibition parameter k as a bifurcation parameter, the numerical Hopf bifurcation analysis shows that p = a + b - 2ac/[x* (1 + kx*2)] [less-than or equal to] 0 is a sufficient and necessary condition, when k increases the period of limit cycle decreases.