一类多项式系统的中心焦点及Hopf分支问题

The Problem of Center or Focus and Hopf Bifurcation for a Class of Polynomical Systems

文章研究了一类多项式系统:dx/dt=-y+δx+lx2+mxy+ax3,dy/dt=x+b1xy+b2xy2+…+bnxyn(bn≠0)基于Liapunov形式级数法理论,得到了O(0,0)是该系统的焦点或中心的一个充分条件,同时分析了该系统依赖于参数δ的Hopf分支问题其补充了文献[5]的结论。

A class of polynomical systems:dx/dt=-y+δx+lx2+mxy+ax3,dy/dt=x+b1xy+b2xy2+…+bnxyn(bn≠0) are investigated in this paper.Based on Liapunov method theory,one sufficient condition for O(0,0) as center or focus is obtained.At the same time,the problem of Hopf bifurcation depending on the parameter δ is analyzed.As a result,the results in literature [5] are supplemented.