Detection of time delays and directional interactions based on time series from complex dynamical systems

Abstract

Data-based and model-free accurate identification of intrinsic time delays and directional interactions is an extremely challenging problem in complex dynamical systems and their networks reconstruction. A model-free method with new scores is proposed to be generally capable of detecting single, multiple, and distributed time delays. The method is applicable not only to mutually interacting dynamical variables but also to self-interacting variables in a time-delayed feedback loop. Validation of the method is carried out using physical, biological, and ecological models and real data sets. Especially, applying the method to air pollution data and hospital admission records of cardiovascular diseases in Hong Kong reveals the major air pollutants as a cause of the diseases and, more importantly, it uncovers a hidden time delay (about 30-40 days) in the causal influence that previous studies failed to detect. The proposed method is expected to be universally applicable to ascertaining and quantifying subtle interactions (e.g., causation) in complex systems arising from a broad range of disciplines.

Partial cross mapping eliminates indirect causal influences

“…If only two variables interact in one direction and the third one is isolated ( Fig. 1a), then the previous methods can be effective for identifying the direct causal link [16][17][18][19][20][21] . However, when the three variables constitute a unidirectional causal chain ( Fig.…”

“…These parameters of embedding dimensions and time lags can be computationally determined by the method of false nearest neighbor (FNN) and delayed mutual information (DMI), respectively. More advanced techniques can also be utilized 20,42 . In general, for any pair of variables ξ and η ∈ {x, y, z}, we set Fig.…”

“…Here system details are typically not known, but only time series are available. Correctly identifying causal relations among the dynamical variables generating the time series provides a window through which the inner dynamics of the target system may be probed into, and a number of previous methods were developed, such as those based on the celebrated Granger causality [1][2][3][4][5] , the entropy [6][7][8][9][10][11] , the dynamical Bayesian inference [12][13][14][15] , and the mutual cross mapping (MCM) [16][17][18][19][20][21] , with applications to real-world systems 5,7,[22][23][24][25][26][27][28][29][30][31] . If the system contains two independent variables only, the causal relation between them is straightforwardly direct.…”

Delay models for the early embryonic cell cycle oscillator

“…The detection of time delays has received considerable interest, expecially in system exhibiting chaotic dynamics [ 61 – 63 ]. Extracting time delays between different interacting variables from such time series can be done in a variety of ways: both simple heuristics and sophisticated algorithms exist [ 64 ]. This is an important topic to study in order to bring the delay models closer to experiments.…”

Реконструкция Ансамблей Осцилляторов С Нелинейными Запаздывающими Связями

“…Задача реконструкции модельных уравнений и определения параметров колебательных систем по их экспериментальным временным рядам актуальна для многих научных дисциплин [1]. Для решения этой задачи разработаны различные методы, причем в последние годы все большее внимание уделяется реконструкции не отдельных систем, а ансамблей связанных между собой осцилляторов [2][3][4][5][6][7][8]. При этом помимо восстановления собственных параметров элементов ансамбля возникает задача выявления наличия, структуры и характеристик связей между элементами.…”