Title: A General Approach to Synchronization of Coupled Cells
Authors: Shih, Chih-Wen
Tseng, Jui-Pin
Department of Applied Mathematics
Keywords: coupled system;synchronization;delay;gene regulation model;neuronal model;neural network
Issue Date: 2013
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 network-scale-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.
URI: http://hdl.handle.net/11536/22819
ISSN: 1536-0040
DOI: 10.1137/130907720
Volume: 12
Issue: 3
Begin Page: 1354
End Page: 1393
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