Möbius group actions in the solvable chimera model

Abstract

We study actions of Möbius group on two sub-populations in the solvable chimera model proposed by Abrams et al. Dynamics of global variables are given by two coupled Watanabe-Strogatz systems, one for each sub-population. At the first glance, asymptotic dynamics in the model seem to be very simple. For instance, in the stable chimera state distributions of oscillators perform a simple rotations after a certain (sufficiently large) moment. However, a closer look unveils that dynamics are subtler that what can be observed from evolution of densities of oscillators' phases. In order to gain the full picture, one needs to investigate dynamics on the transformation group that acts on these densities. Such an approach emphasizes impact of the "hidden" variable that is not visible on macroscopic level.

References in corpus (6)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators
• Partially integrable dynamics of hierarchical populations of coupled oscillators
• Hyperbolic Geometry of Kuramoto Oscillator Networks
• Hyperbolic geometrical optics: Hyperbolic glass

Cited by in corpus (1)

• Phase holonomy underlies puzzling temporal patterns in Kuramoto models with two sub-populations