Identifying the net information flow direction pattern in mutually coupled non-identical chaotic oscillators

TL;DR

This study investigates the direction of information flow in mutually coupled non-identical chaotic oscillators, revealing that the net information transfer predominantly occurs from the more chaotic to the less chaotic oscillator, regardless of their functional forms or phase space dimensions.

Contribution

The paper introduces a model-free asymmetric index based on conditional mutual information and demonstrates its effectiveness across various oscillator configurations.

Findings

Net information flow is from higher to lower chaos oscillator.

Results are consistent across different oscillator types and dimensions.

Supports broad applicability of the proposed information flow pattern.

Abstract

This paper focuses on a fundamental inquiry in a coupled oscillator model framework. It specifically addresses the direction of net information flow in mutually coupled non-identical chaotic oscillators. Adopting a specific form of conditional mutual information as a model-free and asymmetric index, we establish that if the magnitude of the maximum Lyapunov exponent can be defined as the 'degree of chaos' of a given isolated chaotic system, a predominant net information transfer exists from the oscillator exhibiting a higher degree of chaos to the other while they are coupled. We incorporate two distinct categories of coupled 'non-identical' oscillators to strengthen our claim. In the first category, both oscillators share identical functional forms, differing solely in one parameter value. We also adopt another measure, the Liang-Kleeman information flow, to support the generality of our results. The functional forms of the interacting oscillators are entirely different in the second category. We further extend our study to the coupled oscillator models, where the interacting oscillators possess different dimensions in phase space. These comprehensive analyses support the broad applicability of our results.