Multifaceted dynamics of Janus oscillator networks

TL;DR

This paper introduces simple Janus oscillator networks that simultaneously display multiple complex synchronization phenomena, including explosive synchronization, chimera states, and asymmetry-induced synchronization, under minimal and local connectivity conditions.

Contribution

The study demonstrates that Janus oscillator networks can exhibit multiple complex synchronization phenomena concurrently, a novel finding that broadens understanding of network dynamics.

Findings

Networks exhibit explosive synchronization with identical oscillators.

Networks show multistability of chimera states, including traveling and bouncing types.

Synchronization can be promoted by heterogeneity, contrary to typical expectations.

Abstract

Recent research has led to the discovery of fundamental new phenomena in network synchronization, including chimera states, explosive synchronization, and asymmetry-induced synchronization. Each of these phenomena has thus far been observed only in systems designed to exhibit that one phenomenon, which raises the questions of whether they are mutually compatible and, if so, under what conditions they co-occur. Here, we introduce a class of remarkably simple oscillator networks that concurrently exhibit all of these phenomena. The dynamical units consist of pairs of nonidentical phase oscillators, which we refer to as Janus oscillators by analogy with Janus particles and the mythological figure from which their name is derived. In contrast to previous studies, these networks exhibit (i) explosive synchronization with identical oscillators; (ii) extreme multistability of chimera states, including traveling, intermittent, and bouncing chimeras; and (iii) asymmetry-induced synchronization in which synchronization is promoted by random oscillator heterogeneity. These networks also exhibit the previously unobserved possibility of inverted synchronization transitions, in which a transition to a more synchronous state is induced by a reduction rather than an increase in the coupling strength. These various phenomena are shown to emerge under rather parsimonious conditions, and even in locally connected ring topologies, which has the potential to facilitate their use to control and manipulate synchronization in experiments.