Open AccessA NEW TYPE OF BOUNDARY CRISES: CHAOTIC BOUNDARY CRISES
Author(s) -
Hong Liu,
Jianxue Xu
Publication year - 2001
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.50.612
Subject(s) - attractor , chaotic , crisis , saddle , boundary (topology) , chaotic hysteresis , fractal , physics , nonlinear system , boundary value problem , bifurcation , statistical physics , mathematical analysis , synchronization of chaos , computer science , mathematics , control theory (sociology) , quantum mechanics , mathematical optimization , control (management) , artificial intelligence
Crises of chaotic attractors are typical phenomena in nonlinear dynamical systems. By means of generalized cell mapping digraph (GCMD) method, we show that a chaotic boundary crisis results from a collision between a chaotic attractor and a chaotic saddle in the fractal basin boundary. In such a case the chaotic attractor, together with its basin of attraction, is suddenly destroyed as the parameter passes through a critical value, simultaneously the chaotic saddle also undergoes an abrupt enlargement in its size.