Open AccessSTRANGE REPELLER INDUCED BY DYNAMICAL DISCONTINUITY
Author(s) -
S. Xian,
Da-Ren He
Publication year - 1997
Publication title -
acta physica sinica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.46.1307
Subject(s) - attractor , discontinuity (linguistics) , chaotic , physics , orbit (dynamics) , crisis , statistical physics , classical mechanics , nonlinear system , bifurcation , computer science , mathematical analysis , quantum mechanics , mathematics , artificial intelligence , engineering , aerospace engineering
Employing a kind of piece-wise linear map with a hole,we show that “hole-induced crisis” is a result of the emergence of a “strange repeller due to discontinuity”. The strange repeller forces the iteration orbit to escape from the original chaotic attractor.Thus the attactor suddenly expands.We have proved that the lifetime of iterations in original attractor is inversely proportional to the escaping ratio,which enables us to obtain the dependence of the mean lifetime on the control parameter analytically.
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