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Transient and equilibrium causal effects in coupled oscillators.

Dmitry A Smirnov1

  • 1Saratov Branch, V.A. Kotel'nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, 38 Zelyonaya Street, Saratov 410019, Russia.

Chaos (Woodbury, N.Y.)
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Summary
This summary is machine-generated.

This study distinguishes transient and equilibrium causal effects in driven systems. It derives relationships between these effects for coupled oscillators, enabling estimation of equilibrium causality from time series data.

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Area of Science:

  • Complex Systems
  • Dynamical Systems Theory
  • Statistical Mechanics

Background:

  • Causality in complex systems is often categorized into transient and equilibrium effects.
  • Transient causality, observable in time series, is well-modeled by Wiener-Granger causality.
  • Equilibrium causality, reflecting long-term system dynamics, is typically difficult to estimate from fixed-parameter time series.

Purpose of the Study:

  • To investigate the relationship between transient and equilibrium causal effects.
  • To develop methods for estimating equilibrium causality from observed time series data.
  • To analyze these causal effects in unidirectionally coupled stochastic linear oscillators.

Main Methods:

  • Analysis of transient causal effects using Wiener-Granger causality framework.
  • Derivation of approximate closed-form expressions for relationships between transient and equilibrium causality.
  • Modeling of unidirectionally coupled stochastic linear oscillators with varying frequencies and damping factors.

Main Results:

  • Established relationships between transient and equilibrium causal effects for coupled oscillators.
  • Derived approximate analytical expressions quantifying these relationships.
  • Demonstrated the potential for extracting equilibrium causal effects from time series data.

Conclusions:

  • The derived relationships provide a bridge between easily observable transient effects and the often more significant equilibrium effects.
  • The findings offer practical methods for estimating equilibrium causality in systems where direct measurement is challenging.
  • This work advances the understanding and estimation of causality in complex dynamical systems.