Enhancing the stability of the synchronization of multivariable coupled oscillators

TL;DR

This paper investigates how transferring coupling variables affects the stability of synchronization in multivariable oscillator networks, identifying optimal transfer conditions and validating findings through electronic circuit experiments.

Contribution

It introduces a formalism to assess stability under variable coupling transfer and demonstrates an optimal transfer strategy for enhancing synchronization stability.

Findings

Existence of an optimal coupling transfer maximizing stability

Master stability function formalism applied to multivariable coupling

Experimental validation with nonlinear electronic circuits

Abstract

Synchronization processes in populations of identical networked oscillators are in the focus of intense studies in physical, biological, technological and social systems. Here we analyze the stability of the synchronization of a network of oscillators coupled through different variables. Under the assumption of an equal topology of connections for all variables, the master stability function formalism allows assessing and quantifying the stability properties of the synchronization manifold when the coupling is transferred from one variable to another. We report on the existence of an optimal coupling transference that maximizes the stability of the synchronous state in a network of R\"ossler-like oscillators. Finally, we design an experimental implementation (using nonlinear electronic circuits) which grounds the robustness of the theoretical predictions against parameter mismatches, as well as against intrinsic noise of the system.