Two Mechanisms of Remote Synchronization in a Chain of Stuart-Landau Oscillators

TL;DR

This paper investigates how remote synchronization occurs in a chain of Stuart-Landau oscillators, identifying key mechanisms like non-isochronicity and second-order coupling that promote this phenomenon.

Contribution

It provides an analytical framework explaining the mechanisms of remote synchronization using high-order phase reduction in small oscillator networks.

Findings

Analytical demonstration of two factors promoting remote synchrony.

Good agreement between theory and numerical simulations.

Identification of non-isochronicity and second-order coupling as key mechanisms.

Abstract

Remote synchronization implies that oscillators interacting not directly but via an additional unit (hub) adjust their frequencies and exhibit frequency locking while the hub remains asynchronous. In this paper, we analyze the mechanisms of remote synchrony in a small network of three coupled Stuart-Landau oscillators using recent results on high-order phase reduction. We analytically demonstrate the role of two factors promoting remote synchrony. These factors are the non-isochronicity of oscillators and the coupling terms appearing in the second-order phase approximation. We show a good correspondence between our theory and numerical results for small and moderate coupling strengths.