C-oscillators and stability of stationary cluster structures in lattices of diffusively coupled oscillators

Nikolai N. Verichev, Stanislav N. Verichev, Marian Wiercigroch*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

Abstract

This paper studies the conditions for existence and stability of stationary cluster structures in lattices of diffusively coupled dynamical systems within the framework of a new interpretation of cluster synchronization as classical synchronization of cluster oscillators (C-oscillators). The study of existence of cluster attractors is based on the linear chains of cluster oscillators, defining possible types of cluster structures in chains. First, we present interval estimates for the range of coupling strengths in which cluster attractors can exist. Then we formulate and prove the basic theorems about the local stability of the various cluster structures. The presented methodology can be extended to study cluster structures on lattices of different geometry and forms such as linear cluster structures in two-dimensional lattices, layered cluster structures in three-dimensional lattices and cluster structures in ring-shaped systems. Crown

Original languageEnglish
Pages (from-to)686-701
Number of pages16
JournalChaos, Solitons and Fractals
Volume42
Issue number2
DOIs
Publication statusPublished - 30 Oct 2009

Bibliographical note

Funding Information:
The authors thank Dr. Jan Sieber of the University of Aberdeen for valuable discussions and comments. This work was partly supported by the Russian Foundation for Basic Research (project N 09-01-00873). This support is highly appreciated.

Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.

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