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arXiv · 2010.09131

Network and Phase Symmetries Reveal That Amplitude Dynamics Stabilize Decoupled Oscillator Clusters

J. Emenheiser·A. Salova·J. Snyder·J. P. Crutchfield·R. M. D'Souza
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Abstract

Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group, we explore synchronization patterns that emerge from the phase-shift invariance of the dynamical equations and symmetries in the nodes. We show that these nonstructural symmetries simplify stability calculations. We analyze a ring-network of phase-amplitude oscillators that exhibits a "decoupled" state in which physically-coupled nodes appear to act independently due to emergent cancellations in the equations of dynamical evolution. We establish that this state can be linearly stable for a ring of phase-amplitude oscillators, but not for a ring of phase-only oscillators that otherwise require explicit long-range, nonpairwise, or nonphase coupling. In short, amplitude-phase interactions are key to stable synchronization at a distance.

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J. Emenheiser, A. Salova, J. Snyder, J. P. Crutchfield, R. M. D'Souza. 2020-10-18. Network and Phase Symmetries Reveal That Amplitude Dynamics Stabilize Decoupled Oscillator Clusters. https://arxiv.org/abs/2010.09131

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