Symmetric States Requiring System Asymmetry

Abstract

Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the complete synchronization of the entire network is the state inheriting the system symmetry. As in other systems subject to symmetry breaking, such symmetric states are not always stable. Here we report on the discovery of the converse of symmetry breaking--the scenario in which complete synchronization is not stable for identically-coupled identical oscillators but becomes stable when, and only when, the oscillator parameters are judiciously tuned to nonidentical values, thereby breaking the system symmetry to preserve the state symmetry. Aside from demonstrating that diversity can facilitate and even be required for uniformity and consensus, this suggests a mechanism for convergent forms of pattern formation in which initially asymmetric patterns evolve into symmetric ones.

Final proof correction incorporated; 5 pages, 3 figures, Supplemental Material (5 pages, 2 figures); for an animation showing a symmetric state requiring system asymmetry, see http://youtu.be/zP_6EuMzt1I

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• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Turing patterns in network-organized activator-inhibitor systems
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Cited by in corpus (17)

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• Connecting the Kuramoto Model and the Chimera State
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• Introduction to Focus Issue: Patterns of Network Synchronization
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• Experiments with arbitrary networks in time-multiplexed delay systems
• Identical synchronization of nonidentical oscillators: when only birds of different feathers flock together
• Critical Switching in Globally Attractive Chimeras
• Heterogeneity-stabilized homogeneous states in driven media
• Synchronization of coupled metronomes on two layers
• Solitary states in complex networks: impact of topology
• Quasi-symmetries in complex networks: a dynamical model approach
• Concurrent formation of nearly synchronous clusters in each intertwined cluster set with parameter mismatches
• Coupling conditions for globally stable and robust synchrony of chaotic systems
• Individual-level evolutions manifest population-level scaling in complex supply networks
• Steady State Statistics of Emergent Patterns in a Ring of Oscillators
• Optimal cost tuning of frustration: Achieving desired states in the Kuramoto-Sakaguchi model