The Bellerophon state: a novel coherent phase of globally coupled oscillators

Abstract

From rhythmic physiological processes to the collective behaviors of technological and natural networks, coherent phases of interacting oscillators are the foundation of the events' coordination leading a system to behave cooperatively. We unveil the existence of a new of such states, occurring in globally coupled nonidentical oscillators in the proximity of the point where the transition from the system's incoherent to coherent phase converts from explosive to continuous. In such a state, oscillators form quantized clusters, where they are neither phase- nor frequency-locked. Oscillators' instantaneous speeds are different within the clusters, but they form a characteristic cusped pattern and, more importantly, they behave periodically in time so that their average values are the same. Given its intrinsic specular nature with respect to the recently introduced Chimera states, the phase is termed the {\it Bellerophon} state. We provide analytical and numerical description of the microscopic and macroscopic details of {\it Bellerophon} states, thus furnishing practical hints on how to seek for the new phase in a variety of experimental and natural systems.

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• Collective dynamics of heterogeneously and nonlinearly coupled phase oscillators
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• Enlarged Kuramoto Model: Secondary Instability and Transition to Collective Chaos
• Enhancing network synchronization by phase modulation
• Universal scaling and phase transitions of coupled phase oscillator populations
• Reduction of oscillator dynamics on complex networks to dynamics on complete graphs through virtual frequencies
• Cluster-Mediated Synchronization Dynamics in Globally Coupled Oscillators with Inertia
• Classification of bifurcation diagrams in coupled phase-oscillator models with asymmetric natural frequency distributions
• Novel transition and Bellerophon state in coupled Stuart-Landau oscillators