Study of the Wada fractal boundary and indeterminate crisis

• 来源期刊: 中国物理（英文版）
• 学科: 物理学
• 关键词: global analysis generalized cell mapping indeterminate chaotic boundary crisis chaoticsaddle Wada fractal boundary
• 年，卷（期）: 2002,（11）
• 页码范围: 1115-1123
• 页数: 9页
• 分类号: O4
• 语种: 英文

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 boundaries.After a final escape bifurcation, there only exists the attractor at infinity; a chaotic saddle with a beautiful pattern isleft behind in phase space.