A general approach to synchronization of coupled cells

Chih-Wen Shih*, Jui Pin Tseng

*Corresponding author for this work

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

This investigation presents a general framework to establish synchronization of coupled cells and coupled systems. Each individual subsystem is represented by nonlinear differential equations with or without internal or intracellular delay. A general coupling function is employed to depict the communication or interaction between subsystems or cells. Under this framework, the problem of establishing the synchronization for delayed coupled nonlinear systems is transformed to solving a corresponding linear system of algebraic equations. We start by considering a cell-to-cell system under symmetric coupling to present the main idea of the approach. The framework is then extended to the N-cell system under circulant coupling. Delay-dependent, delay-independent, and networkscale-dependent criteria for global synchronization will be established, respectively. The developed scheme can accommodate a wide range of coupled systems. We demonstrate the applications of the present approach to establish synchronization for a gene regulation model, a neuronal model, and some neural networks.

Original languageEnglish
Pages (from-to)1354-1393
Number of pages40
JournalSIAM Journal on Applied Dynamical Systems
Volume12
Issue number3
DOIs
StatePublished - 8 Oct 2013

Keywords

  • Coupled system
  • Delay
  • Gene regulation model
  • Neural network
  • Neuronal model
  • Synchronization

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