Coupled Moebius Maps as a Tool to Model Kuramoto Phase Synchronization
arXiv:2001.07593 · doi:10.1103/PhysRevE.102.022206
Abstract
We propose Moebius maps as a tool to model synchronization phenomena in coupled phase oscillators. Not only does the map provide fast computation of phase synchronization, it also reflects the underlying group structure of the sinusoidally coupled continuous phase dynamics. We study map versions of various known continuous-time collective dynamics, such as the synchronization transition in the Kuramoto-Sakaguchi model of non-identical oscillators, chimeras in two coupled populations of identical phase oscillators, and Kuramoto-Battogtokh chimeras on a ring, and demonstrate similarities and differences between the iterated map models and their known continuous-time counterparts.
arXiv comment13 pages, 4 figures
References in corpus (15)
- Chimera States for Coupled Oscillators
- Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
- Solvable model for chimera states of coupled oscillators
- Partially integrable dynamics of hierarchical populations of coupled oscillators
- Phase oscillators with global sinusoidal coupling evolve by Mobius group action
- Low-dimensional dynamics of populations of pulse-coupled oscillators
- Basins of Attraction for Chimera States
- Cascades of Multi-headed Chimera States for Coupled Phase Oscillators
- Kuramoto model for excitation-inhibition-based oscillations
- Hyperbolic Geometry of Kuramoto Oscillator Networks
- Low-Dimensional Dynamics for Higher Order Harmonic Globally Coupled Phase Oscillator Ensemble
- Synchronisation in Coupled Sine Circle Maps
- Repulsively Coupled Kuramoto-Sakaguchi Phase Oscillators Ensemble Subject to Common Noise
- A robust autoassociative memory with coupled networks of Kuramoto-type oscillators
- Chimera states and the interplay between initial conditions and non-local coupling