Reveal That

Amplitude Dynamics Stabilize Decoupled Oscillator Clusters

Jeffrey Emenheiser, |

**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.

J. Emenheiser, A. Salova, J. Snyder, J. P. Crutchfield, and R. M. D'Souza, “Network and Phase Symmetries Reveal That Amplitude Dynamics Stabilize Decoupled Oscillator Clusters” (2020) .

doi:.

[pdf]

arxiv.org:2010.09131.