FITZHUGH神经传导方程中的HOPF分支

Hopf Bifurcation of Fitzhugh's Nerve Conduction Equation

本文讨论Fitzhugh神经传导方程 (dx)/(dt)=α+x+y-/1/3x^3,(dy)/(dt)=ρ(A-x-By)的Hopf分支问题,其中α,A∈(-∞,+∞),A,B∈(0,1)都是实参数。笔者得出了此方程关于每个参数的Hopf分支命题,给出了各参数分支值的显示或隐示表达式,并指出极限环随各参数变化的趋势。

Hopef bifurcation of Fitzhugh's nerve conduction equation is dealt with dx/dy= α+x+y-1/3x^3, dy/dx= ρ(A-x-By) whereα, A∈ ( -∞, +∞), ρ, B∈ (0, 1)are real parameters. The proposition of Hopf bifurcation of this equation for every parameter is obtained. The explicit or implicit expression of bifurcation value of every parameter is given and the variation trends of the limit cycles varying with variation of every parameter are Pointed out.