Couplings in complex real-world systems are often nonlinear and scale-dependent. In many cases, it is crucial to consider a multitude of interlinked variables and the strengths of their correlations to adequately fathom the dynamics of a high-dimensional nonlinear system. We propose a recurrence based dependence measure that quantifies the relationship between multiple time series based on the predictability of their joint evolution. The statistical analysis of recurrence plots (RPs) is a powerful framework in nonlinear time series analysis that has proven to be effective in addressing many fundamental problems, e.g., regime shift detection and identification of couplings. The recurrence flow through an RP exploits artifacts in the formation of diagonal lines, a structure in RPs that reflects periods of predictable dynamics. By using time-delayed variables of a deterministic uni-/multivariate system, lagged dependencies with potentially many time scales can be captured by the recurrence flow measure. Given an RP, no parameters are required for its computation. We showcase the scope of the method for quantifying lagged nonlinear correlations and put a focus on the delay selection problem in time-delay embedding which is often used for attractor reconstruction. The recurrence flow measure of dependence helps to identify non-uniform delays and appears as a promising foundation for a recurrence based state space reconstruction algorithm.
翻译:复杂的现实世界系统中的重叠往往不线性和规模依赖性。 在许多情况下,关键是要考虑众多相互关联的变量及其关联的强项,以充分理解高维非线性系统的动态。 我们建议基于重复依赖性的测量,根据共同演变的可预测性量化多时间序列之间的关系。 复发地块(RP)的统计分析是非线性时间序列分析中的一个强有力的框架,事实证明,它对于解决许多基本问题是有效的,例如,制度转移探测和查明组合。通过RP的复发流动利用了成对角线的工艺,而对角线系是反映可预见动态期的结构。我们建议采用基于时间间隔的单/多变化系统变数序列变数的变数,可以通过复发量测量来捕捉到可能存在许多时间尺度的滞后依赖性。 鉴于RP,不需要任何参数来进行计算。 我们展示了对滞后的非线性关联性识别方法的范围。 RP的重现过程利用了成的工艺品,在形成对角系线性线性线性线性线性线性线性线性线上,这是RP中的一种结构中的一种结构,这种结构反映可反映可预测性动态动态动态动态动态动态动态动态动态动态动态动态动态动态的时期结构。 通过使用时间延迟的变变的变的变变换的变换的变数,从而使得以吸引性变的重现成为一个周期性变换的基础。 以吸引性变换的基础。 以吸引性变的周期性变的周期性变的周期性变的周期性变的周期性变的周期性变的周期性变换的基础。 以用于为一种不为一种基于的周期性变制的调整性变换的基础,在的调整性变制的调整性变制的调整性变的调整性变。 。 重制的变的调整性变制的调整性变制的变制的变制的变制的变的变制,以为为为为为为一种以以以为为一种以为为为一种不制的调整性变换制制制的调整制制制制制制制制制的变换制的变换制的变换制的变换制的变换制的变换换制的变换制的变换制的调整制的变换制的变换制的