Spatio-temporal dynamics of Kuramoto-Sakaguchi model with time dependent connectivity

Abstract

We have studied the dynamics of the paradigmatic Kuramoto-Sakaguchi model of identical coupled phase oscilla- tors with various kinds of time-dependent connectivity using Eulerian discretization. We first explore the parameter spaces for various types of collective states using the phase plots of the two statistical quantities, namely the strength of incoherence and the discontinity measure. In the quasi-static limit of the changing of coupling range, we have observed how the system relaxes from one state to another and have identified a few interesting collective dynamical states along the way. Under a sinusoidal change of the coupling range, the global order parameter characterizing the degree of synchronization in the system is shown to undergo a hysteresis with the coupling range. Finally, we study the low-dimensional spatio-temporal dynamics of the local order parameter in the continuum limit using the recently-developed Ott-Antonsen ansatz and justify some of our numerical results. In particular, we identify an intrinsic time-scale of the Kuramoto system and show that the simulations exhibit two distinct kinds of qualitative behavior in two cases when the time-scale associated with the switching of the coupling radius is very large compared to the intrinsic time-scale and when it is comparable with the intrinsic time-scale.

10 Pages Latex (including 10 captioned figures)

References in corpus (10)

• Statistical physics of social dynamics
• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Analysis of a power grid using the Kuramoto-like model
• Observation and characterization of chimera states in coupled dynamical systems with nonlocal coupling
• Sub-femtosecond synchronization of microwave oscillators with mode-locked Er-fiber lasers
• Hysteretic transitions in the Kuramoto model with inertia
• External Periodic Driving of Large Systems of Globally Coupled Phase Oscillators
• First experimental observation of generalized synchronization phenomena in microwave oscillators
• Low-dimensional behavior of Kuramoto model with inertia in complex networks

Cited by in corpus (3)

• Transient Chaos Generates Small Chimeras
• Spontaneous collective synchronization in the Kuramoto model with additional non-local interactions
• Cellular Automata Model of Synchronization in Coupled Oscillators