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

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. Subsequently, the calculation of projected Kolmogorov-Sinai entropy for variables associated with the interacting oscillators reveals that the oscillator exhibiting a higher degree of chaos is also characterized by a higher projected Kolmogorov-Sinai entropy value and transfers more information to the other oscillator. 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.