一类分段光滑映象中有新特征的激变

CRISES WITH SPECIAL SCALING PROPERTIES IN PEICE\|WISE\|SMOOTH SYSTEMS 

讨论了描述一类电子张弛振子的分段光滑映象中的两种不连续性导致激变的特性．一种激变发生的机理是一个混沌吸引子吸引域内的不稳定周期轨道与映象的不连续区碰撞；而另一种激变的机理是一个混沌吸引子与两个映象的不连续区构成的“映孔”碰撞．发现第一种激变的平均层流相长度的标度律为〈τ〉∝－ １８ ，层流相长度分布的标度律为Ｐ（ τ） ＝ １〈τ〉·ｅｘｐ － τ〈τ〉 ，而第二种激变的标度律分别为〈τ〉∝ｅｘｐ（ ｋ－ １／２） 和Ｐ（ τ） ＝ １〈τ〉ｅｘｐ － τ〈τ〉 ．

Two kinds of crises with speciality properties in piece\|wise\|smooth systems are reported. The crises are induced by the discontinuity of the systems. The mechanism of the first kind of crisis is a collision between a forbiden region and an unstable orbit located in the region of chaotic attractor. On the contrary, the second one is produced by the collision between a chaotic attractor and a hole induced by the discontinuous regions of the system. For the first one, the scaling laws of the average laminar lenths and its distribution are 〈τ〉∝ -1\^8 and P(τ)=1〈τ〉 exp -τ/〈τ〉, respectively. Meanwhile, for the second one, the scaling laws are 〈τ〉∝ exp( k -1/2 ) and P(τ)=1〈τ〉· exp-τ/〈τ〉).