Coexistence of Hamiltonian-like and dissipative dynamics in chains of coupled phase oscillators with skew-symmetric coupling

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Date
2017
Volume
2447
Issue
Journal
Series Titel
WIAS Preprints
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract

We consider rings of coupled phase oscillators with anisotropic coupling. When the coupling is skew-symmetric, i.e. when the anisotropy is balanced in a specific way, the system shows robustly a coexistence of Hamiltonian-like and dissipative regions in the phase space. We relate this phenomenon to the time-reversibility property of the system. The geometry of low-dimensional systems up to five oscillators is described in detail. In particular, we show that the boundary between the dissipative and Hamiltonian-like regions consists of families of heteroclinic connections. For larger chains with skew-symmetric coupling, some sufficient conditions for the coexistence are provided, and in the limit of N oscillators, we formally derive an amplitude equation for solutions in the neighborhood of the synchronous solution. It has the form of a nonlinear Schrödinger equation and describes the Hamiltonian-like region existing around the synchronous state similarly to the case of finite rings.

Description
Keywords
Phase oscillators, reversible systems, amplitude equations
Citation
Burylko, O., Mielke, A., Wolfrum, M., & Yanchuk, S. (2017). Coexistence of Hamiltonian-like and dissipative dynamics in chains of coupled phase oscillators with skew-symmetric coupling (Vol. 2447). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2447
License
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