Bistability of patterns of synchrony in Kuramoto oscillators with inertia
Abstract
We study the co-existence of stable patterns of synchrony in two coupled populations of identical Kuramoto oscillators with inertia. The two populations have different sizes and can split into two clusters where the oscillators synchronize within a cluster while there is a phase shift between the dynamics of the two clusters. Due to the presence of inertia, which increases the dimensionality of the oscillator dynamics, this phase shift can oscillate, inducing a breathing cluster pattern. We derive analytical conditions for the co-existence of stable two-cluster patterns with constant and oscillating phase shifts. We demonstrate that the dynamics, that governs the bistability of the phase shifts, is described by a driven pendulum equation. We also discuss the implications of our stability results to the stability of chimeras.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Aug 24, 2016
- Source ID
- 10.1063/1.4961435
Entities
People
- Barrett N. Brister
- Igor V. Belykh
- Vladimir N. Belykh
Organizations
- Army Research Office
- Georgia State University
- N. I. Lobachevsky State University of Nizhny Novgorod
- National Science Foundation
- Russian Center for Science Information
- Russian Science Foundation
- Volga State University of Water Transport