Olivares F, Zanin M, Zunino L, Pérez D G
Instituto de Física, Pontificia Universidad Católica de Valparaiso (PUCV), 23-40025 Valparaíso, Chile.
Centro de Tecnología Biomédica, Universidad Politécnica de Madrid, Campus de Montegancedo, Pozuelo de Alarcón, 28223 Madrid, Spain.
Chaos. 2020 Jun;30(6):063101. doi: 10.1063/1.5142500.
We introduce a representation space to contrast chaotic with stochastic dynamics. Following the complex network representation of a time series through ordinal pattern transitions, we propose to assign each system a position in a two-dimensional plane defined by the permutation entropy of the network (global network quantifier) and the minimum value of the permutation entropy of the nodes (local network quantifier). The numerical analysis of representative chaotic maps and stochastic systems shows that the proposed approach is able to distinguish linear from non-linear dynamical systems by different planar locations. Additionally, we show that this characterization is robust when observational noise is considered. Experimental applications allow us to validate the numerical findings and to conclude that this approach is useful in practical contexts.
我们引入一个表示空间来对比混沌动力学与随机动力学。通过序数模式转换对时间序列进行复杂网络表示后，我们建议为每个系统在一个二维平面中指定一个位置，该平面由网络的排列熵（全局网络量化指标）和节点排列熵的最小值（局部网络量化指标）定义。对代表性混沌映射和随机系统的数值分析表明，所提出的方法能够通过不同的平面位置区分线性和非线性动力系统。此外，我们表明，当考虑观测噪声时，这种表征是稳健的。实验应用使我们能够验证数值结果，并得出结论：这种方法在实际应用中是有用的。
