Open AccessCRISES WITH SPECIAL SCALING PROPERTIES IN PEICE-WISE-SMOOTH SYSTEMS
Author(s) -
Shaochuan Wu,
Xilun Ding,
Daihai He
Publication year - 1999
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.48.2180
Subject(s) - attractor , scaling , discontinuity (linguistics) , chaotic , collision , scaling law , physics , statistical physics , orbit (dynamics) , mathematical analysis , mathematics , computer science , geometry , computer security , artificial intelligence , engineering , aerospace engineering
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〉).