1. Network and Phase Symmetries Reveal That Amplitude Dynamics Stabilize Decoupled Oscillator Clusters
- Author
-
Emenheiser, J., Salova, A., Snyder, J., Crutchfield, J. P., and D'Souza, R. M.
- Subjects
Mathematics - Dynamical Systems ,Nonlinear Sciences - Chaotic Dynamics ,Nonlinear Sciences - Pattern Formation and Solitons - 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., Comment: 8 pages, 4 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/gamma_sync.htm
- Published
- 2020