Detection of coupling in Duffing oscillator systems

TL;DR

This paper presents a method using conditional mutual information to detect and infer the direction and strength of coupling in Duffing oscillator systems across regular and chaotic regimes.

Contribution

It introduces a novel approach employing CMI and information susceptibility to identify coupling direction and parameters in complex dynamical systems.

Findings

CMI successfully infers coupling direction in Duffing oscillators.

Information susceptibility estimates coupling strength in weak coupling regimes.

Method applies to both regular and chaotic dynamical states.

Abstract

In complex dynamical systems, the detection of coupling and its direction from observed time series is a challenging task. We study coupling in coupled Duffing oscillator systems in regular and chaotic dynamical regimes. By observing the conditional mutual information (CMI) based on the Shannon entropy, we successfully infer the direction of coupling for different system regimes. Moreover, we show that in the weak coupling limit the values of CMI can be used to infer the coupling parameters by computing the derivative of the conditional mutual information with respect to the coupling strength, called the information susceptibility. The complete numerical implementation is available at https://repo.ijs.si/mbresar/duffing-cmi.