Stability of synchronization in a shift-invariant ring of mutually coupled oscillators
type: Item
instance of: scholarly article
title: Stability of synchronization in a shift-invariant ring of mutually coupled oscillators
zbMATH Open document ID: 1184.34061
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2008-10-30T00:00:00Z
review text: Starting with a shift-invariant ring of \(N\) mutually coupled self-sustained electrical units, the authors come to consideration of the system of \(N\) nearest neighbour coupled identical Rayleigh-Duffing oscillators \[ \ddot{x}_n - \mu (1 - \dot{x}_n^2) \dot{x}_n + x_n + \beta x_n^3 = K (x_{n+1}-2 x_n + x_ {n-1}),\quad n=1,\dots,N, \] where \(\mu\), \(\beta\) and \(K\) are system parameters. For this system, they perform linear stability analysis of completely synchronized \(T\)-periodic solutions. Exploiting the translation symmetry of the system, they develop a qualitative theory for the Lyapunov exponents which relates to some extent to the Master stability function approach. Theoretical predictions about the stability of synchronous regime are compared with the results of numerics on the corresponding dynamical systems.
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34D08
Mathematics Subject Classification ID: 37N20
Mathematics Subject Classification ID: 34D06
zbMATH DE Number: 5359472
zbMATH Keywords: ring of coupled oscillators
zbMATH Keywords: synchronization
zbMATH Keywords: periodic solutions
zbMATH Keywords: Master stability function
zbMATH Keywords: Lyapunov exponents
author: René Yamapi
author: Robert S. MacKay
reviewed by: Oleh Omel'chenko
MaRDI profile type: Publication
full work available at URL: dcdsb.2008.10.973
OpenAlex ID: W2150101792
DOI: 10.3934/DCDSB.2008.10.973
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description: scientific article; zbMATH DE number 5359472