Study of the Wada fractal boundary and indeterminate crisis
作者机构：Institute of Nonlinear Dynamics Xi'an Jiaotong University Xi'an 710049 China
出 版 物：《Chinese Physics B》 (中国物理B（英文版）)
年 卷 期：2002年第11卷第11期
页 面：1115-1123页
核心收录：
学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学]
基 金：the National Natural Science Foundation of China (Grant 10172067 and 19972051)
主 题：global analysis generalized cell mapping indeterminate chaotic boundary crisis chaoticsaddle Wada fractal boundary
摘 要：By using the generalized cell mapping digraph (GCMD) method, we study bifurcations governing the escape ofperiodically forced oscillators in a potential well, in which a chaotic saddle plays an extremely important role. In thispaper, we find the chaotic saddle, and we demonstrate that the chaotic saddle is embedded in a strange fractal boundarywhich has the Wada property, that any point on the boundary of that basin is also simultaneously on the boundary ofat least two other basins. The chaotic saddle in the Wada fractal boundary, by colliding with a chaotic attractor, leadsto a chaotic boundary/crisis with a global indeterminate outcome which presents an extreme form of indeterminacy ina dynamical system ./We also investigate the origin and evolution of the chaotic saddle in the Wada fractal boundary,particularly concentrating on its discontinuous bifurcations (metamorphoses). We demonstrate that the chaotic saddlein the Wada fractal boundary is created by the collision between two chaotic saddles in different fractal *** a final escape bifurcation, there only exists the attractor at infinity; a chaotic saddle with a beautiful pattern isleft behind in phase space.
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