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.
- Received 17 July 2018
- Revised 12 October 2018
DOI:https://doi.org/10.1103/PhysRevX.9.011017
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Synopsis
SynopsisThe Complex Dance of Two-Faced Oscillators
Published 30 January 2019
A ring of “Janus” oscillators—oscillators made from two components with differing natural frequencies—can exhibit myriad synchronization patterns.
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Popular Summary
Spontaneous synchronization, the process in which interacting entities keep pace with each other, underlies the workings of numerous physical and biological systems, from coupled lasers to neural circuits. While researchers have identified a plethora of synchronization phenomena in different systems, we wonder if a more unified framework can describe these diverse observations and reveal new behaviors. To approach this question, we introduce a class of remarkably simple oscillator networks that exhibit many synchronization phenomena of recent interest.
The dynamical units in these networks are composed of “Janus oscillators”—pairs of phase oscillators with distinct natural frequencies. Like the eponymous two-faced Roman god, Janus oscillators are characterized by the opposing tendencies of their constituents, which in this case are determined by their different frequencies.
We study networks of interacting Janus oscillators, in which the different Janus oscillators may be identical or different. As the interaction strength and heterogeneity are varied, such a network exhibits a multitude of synchronization phenomena, including (i) chimera states, which consist of coexisting incoherence and synchrony in identically coupled identical oscillators; (ii) explosive synchronization, which occurs when the transition to synchronization becomes abrupt; (iii) asymmetry-induced synchronization, in which oscillator heterogeneity promotes rather than inhibits synchronization; and (iv) inverted synchronization transitions, defined as transitions into a more synchronous state induced by a reduction in the interaction strength.
The structure underlying our model is natural. It appears, for example, in magnetism and biophysics, but it can also be easily engineered in lab experiments. Janus oscillator models are thus expected to offer a unified understanding of synchronization, inspire experimental design, and lead to new discoveries.
