Synchronization facilitated by frequency differences: Dynamics of coupled-oscillator systems with damaged elements

TL;DR

This paper explores how frequency differences can facilitate synchronization in coupled oscillator systems with damaged elements, revealing a reentrant synchronization phenomenon through simulations and theoretical analysis.

Contribution

It introduces a novel understanding that increasing frequency differences can restore synchronization in systems with damaged oscillators, supported by numerical and theoretical methods.

Findings

Synchronization can be reentrant with increasing frequency differences.

Damaged oscillators modeled as damped oscillators influence system dynamics.

Theoretical stability analysis predicts the reentrant synchronization phenomenon.

Abstract

This study investigates the synchronization dynamics of coupled-oscillator systems in which some of the oscillators are damaged and lose their autonomous oscillations. The damaged elements are modeled using damped oscillators; thus, the system is composed of both limit-cycle oscillators and damped oscillators. In this system, as is commonly observed in conventional coupled limit-cycle oscillators, synchronization among oscillators is destroyed when the difference between the natural frequencies of the oscillators increases. However, in the presence of damped oscillators, synchronization can be facilitated by further increasing the frequency difference from the desynchronization state. We conduct numerical simulations on coupled Stuart-Landau oscillators and investigate this reentrance of synchronization systematically. We also propose an approximate theory to predict the stability of the synchronization state based on a linear stability analysis of the fixed point, which reveals the appearance of the Hopf modes. Using this theory, we argue that the reentrance of synchronization driven by increasing frequency differences can be observed in a wide range of coupled-oscillator systems with damaged elements.