不光滑动力系统中的广义Hopf分枝

摘要

@@ The purpose of this paper is to study the Hopf bifurcation property of the non-smooth planar dynamical system(x(t)y(t))={K+(x(t),y(t),ㄚ),if x(t)>0;K-(x(t),y(t),ㄚ),if x(t)<0,(1)rnwhere the individual functions K±:R2×I→R2 at the right-hand side for some interval I containing 0 are smooth enough and given byrnK±(x,y,ㄚ):=A±α(ㄚ)(x,y)T+(g±1(x,y,ㄚ),g±2(x,y,ㄚ))T.