Kacperski K, Hołyst J A
Max Planck Institute for Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Jul;60(1):403-7. doi: 10.1103/physreve.60.403.
Analytical and numerical study of the roughly periodic oscillations emerging on the background of the well-known power law governing the scaling of the average lifetimes of crisis induced chaotic transients is presented. The explicit formula giving the amplitude of "normal" oscillations in terms of the eigenvalues of unstable orbits involved in the crisis is obtained using a simple geometrical model. We also discuss the commonly encountered situation when normal oscillations appear together with "anomalous" ones caused by the fractal structure of basins of attraction.
本文对在著名的幂律背景下出现的大致周期性振荡进行了分析和数值研究，该幂律用于描述危机诱导混沌瞬态平均寿命的标度关系。通过一个简单的几何模型，得到了一个根据危机中涉及的不稳定轨道特征值给出“正常”振荡幅度的显式公式。我们还讨论了常见的情况，即正常振荡与由吸引子盆地的分形结构引起的“异常”振荡同时出现。
