Classification of synchronization in nonlinear systems using ICO learning

TL;DR

This paper explores how ICO learning can classify synchronization states in coupled nonlinear oscillators, revealing distinct weight behaviors in chaotic versus quasiperiodic regimes, thus offering a new classification approach.

Contribution

It demonstrates the application of ICO learning to distinguish synchronization types in nonlinear systems, a novel use of differential Hebbian learning in this context.

Findings

Weights remain constant during anti-phase synchronization despite distortion.

Erratic weight evolution occurs during quasiperiodic dynamics.

ICO learning effectively classifies synchronization regimes.

Abstract

In this work, we investigate the implications of the differential Hebbian learning rule known as Input-Correlations (ICO) learning in the classification of synchronization in coupled nonlinear oscillator systems. We are investigating the parity-time symmetric coupled Duffing oscillator system with nonlinear dissipation/amplification. In our investigation of the temporal dynamics of this system, it is observed that the system exhibits chaotic as well as quasiperiodic dynamics. On further investigation, it is found that the chaotic dynamics is distorted anti-phase synchronized, whereas the quasiperiodic dynamics is desynchronized. So, on the application of the ICO learning in these two parametric regimes, we observe that the weight associated with the stimulus remains constant when the oscillators are anti-phase synchronized, in spite of there being distortion in the synchronization. But when the oscillators exhibit quasiperiodic dynamics, there is erratic evolution of the weight with time. So, from this, it could be ascertained that the ICO learning could be made use of in the classification of synchronization dynamics in nonlinear systems.