“Causometry” of processes in arbitrary dynamical systems: Three levels of directional coupling quantifiers

IF 1.8 4区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

EPL Pub Date : 2024-09-04 DOI:10.1209/0295-5075/ad7285

Dmitry A. Smirnov

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引用次数: 0

Abstract

The concept of dynamical causal effect (DCE) which unites numerous causality quantifiers for processes in dynamical systems (DS) as measures of X-responses to some Y-variations is generalised through updating the definition of the factors constituting those variations. Along with initial states and governing parameters, external driving (noise) realisations are included and all three factors are represented with their probability distributions. Three basic levels of DCEs are introduced based on their resolution with respect to each factor: low (three factors resolved), medium (two factors), and high (one factor). It is shown that i) a directional coupling with zero transfer entropy (a medium-level DCE) may be strong in terms of its low-level DCEs; ii) DCEs of the same level may be small or large depending on their Y-variations, e.g., a coupling which induces synronisation is both weak and strong according to different medium-level DCEs; iii) high-level DCEs allow comparison of couplings from different sources which may be inaccessible via medium-level DCEs. The generalised DCE concept applies to arbitrary DS including deterministic (driven) DS and random DS with any kind of noise.

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任意动态系统中过程的 "因果关系"：三层定向耦合量化器

动态因果效应（DCE）的概念将动态系统（DS）中众多过程的因果关系量化指标统一为对某些 Y 变化的 X 反应的度量，通过更新构成这些变化的因素的定义，DCE 的概念得到了推广。除了初始状态和控制参数外，还包括外部驱动（噪声）现实，所有三个因素都用其概率分布来表示。根据每个因素的分辨率，引入了三个基本级别的 DCE：低（三个因素分辨率）、中（两个因素）和高（一个因素）。研究表明：i) 从低级 DCEs 的角度看，转移熵为零的定向耦合（中级 DCE）可能很强；ii) 同一级别的 DCEs 可能很小，也可能很大，这取决于它们的 Y 变量，例如，根据不同的中级 DCEs，引起同步化的耦合既弱又强；iii) 高级 DCEs 可以比较不同来源的耦合，而中级 DCEs 可能无法比较这些耦合。广义 DCE 概念适用于任意 DS，包括确定性（驱动）DS 和带有任何噪声的随机 DS。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

EPL 物理-物理：综合

CiteScore

3.30

自引率

5.60%

发文量

332

审稿时长

1.9 months

期刊介绍： General physics – physics of elementary particles and fields – nuclear physics – atomic, molecular and optical physics – classical areas of phenomenology – physics of gases, plasmas and electrical discharges – condensed matter – cross-disciplinary physics and related areas of science and technology. Letters submitted to EPL should contain new results, ideas, concepts, experimental methods, theoretical treatments, including those with application potential and be of broad interest and importance to one or several sections of the physics community. The presentation should satisfy the specialist, yet remain understandable to the researchers in other fields through a suitable, clearly written introduction and conclusion (if appropriate). EPL also publishes Comments on Letters previously published in the Journal.