Stalactite basin structure of dynamical systems with transient chaos in an invariant manifold
作者:Vasily Dronov、Edward Ott
DOI:10.1063/1.166495
日期:2000.6
invariant manifold and another attractor not in the invariant manifold. It is found that the boundary separating these basins has an interesting structure: The basin of the attractor not in the invariant manifold is characterized by thin cusp shaped regions ("stalactites") extending down to touch the nonattracting chaotic set in the invariant manifold. We also develop theoretical scalings applicable to
具有不变流形的动力学系统在各种情况下都会发生(例如,相同的耦合振荡器和具有对称性的系统)。我们考虑在不变流形中既有非混沌吸引子(例如,周期性轨道)又有非吸引子混沌集合(或混沌排斥器)的情况。我们考虑了在不变流形中吸引非混沌集和在不变流形中没有吸引子的盆地的特征。已发现分隔这些盆地的边界具有有趣的结构:吸引子的盆地不在不变歧管中,其特征是向下延伸以接触不变歧管中无吸引力的混沌集合的尖尖形区域(“钟乳石”)。我们还开发了适用于这些系统的理论标度,并与数值实验进行比较。(c)2000年美国物理研究所。