Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, AB24 3UE Aberdeen, United Kingdom.
Chaos. 2009 Dec;19(4):043115. doi: 10.1063/1.3263943.
We show a function that fits well the probability density of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space. It deviates from the exponential statistics by a small power-law term, a term that represents the deterministic manifestation of the dynamics. We also show how one can quickly and easily estimate the Kolmogorov-Sinai entropy and the short-term correlation function by realizing observations of high probable returns. Our analyses are performed numerically in the Henon map and experimentally in a Chua's circuit. Finally, we discuss how our approach can be used to treat the data coming from experimental complex systems and for technological applications.
我们展示了一个函数，它很好地拟合了混沌轨迹在相空间中有限区域内两次连续访问之间的返回时间的概率密度。它通过一个小的幂律项偏离了指数统计，这个项代表了动力学的确定性表现。我们还展示了如何通过实现高概率返回的观测，快速轻松地估计柯尔莫哥洛夫-辛钦熵和短期相关函数。我们的分析是在 Henon 映射中进行数值计算，并在 Chua 的电路中进行实验。最后，我们讨论了如何使用我们的方法来处理来自实验复杂系统的数据，并将其应用于技术应用。
