一个分段光滑系统中的特征激变

摘要

报道了一个具有过电压保护的张弛振荡电路,它由两个保守映射不可逆耦合而成的分段光滑映射描述.在这样一个类耗散系统中,当系统的控制参数达到某一阈值时,混沌吸引子突然消失而产生激变.该激变具有两个特征:一是椭圆岛自身构成混沌吸引子逃逸的"选逸孔洞",二是它的标度指数为1.79.%The thesis reports a relaxation and oscillation circuit with over-voltage protection, which is described by a piecewise smooth concatenation of two conservative maps. In such a quasi-dissipative system, crisis arises from the sudden disappearance of a chaotic attractor with fractal dimension when the control parameter reaches a certain threshold value. The crisis has two characteristics: the elliptic island itself is escaping hole through which the chaotic attractor escapes; its scale index is 1.79.