Transient scaling and resurgence of chimera states in networks of Boolean phase oscillators

TL;DR

This paper investigates the transient dynamics and resurgence of chimera states in networks of Boolean phase oscillators, revealing exponential scaling of transient times with network size and the coexistence of order and disorder.

Contribution

It provides the first experimental confirmation of exponential transient scaling in large oscillator networks and links it to phase-space volume effects.

Findings

Transient times grow exponentially with network size.

Chimera states can resurge during network evolution.

Transient dynamics follow a Poisson process.

Abstract

We study networks of non-locally coupled electronic oscillators that can be described approximately by a Kuramoto-like model. The experimental networks show long complex transients from random initial conditions on the route to network synchronization. The transients display complex behaviors, including resurgence of chimera states, which are network dynamics where order and disorder coexists. The spatial domain of the chimera state moves around the network and alternates with desynchronized dynamics. The fast timescale of our oscillators (on the order of $100\;\mathrm{ns}$) allows us to study the scaling of the transient time of large networks of more than a hundred nodes, which has not yet been confirmed previously in an experiment and could potentially be important in many natural networks. We find that the average transient time increases exponentially with the network size and can be modeled as a Poisson process in experiment and simulation. This exponential scaling is a result of a synchronization rate that follows a power law of the phase-space volume.