Open AccessBOUNDARY CRISIS IN A 2D PIECE-WISE SMOOTH MAP*
Author(s) -
Ma Ming-Quan,
Wang Wen-Xiu,
Daihai He
Publication year - 2000
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.49.1679
Subject(s) - attractor , boundary (topology) , eigenvalues and eigenvectors , chaotic , scaling , saddle , node (physics) , scaling law , saddle point , mathematical analysis , physics , computer science , geometry , mathematics , mathematical optimization , quantum mechanics , artificial intelligence
This paper analytically discusses the characteristics of boundary crisis in a mo del of impact oscillator,and proves that the scaling behavior of the life time after crisis follows the rule τ-ε-γ and γ=ln|β2|ln|β1β2|.Here β1 and β2 are the unstab le and stable eigenvalues,respectively,of a saddle node on the basin boundary of a chaotic attractor.This rule is completely different from that in everywhere-s mooth maps.