Departament de Física i Enginyeria Nuclear, Escola Tecnica Superior d'Enginyeries Industrial i Aeronautica de Terrassa, Universitat Politècnica de Catalunya, Colom 11, 08222 Terrassa, Barcelona, Spain.
Philos Trans A Math Phys Eng Sci. 2011 Jan 28;369(1935):425-38. doi: 10.1098/rsta.2010.0281.
Statistical complexity measures are used to quantify the degree of complexity of the delayed logistic map, with linear and nonlinear feedback. We employ two methods for calculating the complexity measures, one with the 'histogram-based' probability distribution function and the other one with ordinal patterns. We show that these methods provide complementary information about the complexity of the delay-induced dynamics: there are parameter regions where the histogram-based complexity is zero while the ordinal pattern complexity is not, and vice versa. We also show that the time series generated from the nonlinear delayed logistic map can present zero missing or forbidden patterns, i.e. all possible ordinal patterns are realized into orbits.
统计复杂度测度被用于量化延迟 logistic 映射的复杂度，其中包括线性和非线性反馈。我们采用了两种方法来计算复杂度测度，一种是基于“直方图”的概率分布函数，另一种是基于有序模式。我们表明，这些方法提供了关于延迟诱导动力学复杂度的互补信息：存在一些参数区域，其中基于直方图的复杂度为零，而有序模式复杂度不为零，反之亦然。我们还表明，从非线性延迟 logistic 映射生成的时间序列可以呈现零缺失或禁止模式，即所有可能的有序模式都在轨道中实现。
