4.7 Article

The fractional-order modeling and synchronization of electrically coupled neuron systems

Journal

COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 64, Issue 10, Pages 3329-3339

Publisher

PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2012.01.005

Keywords

Non-standard Finite deference scheme; Fractional differential equation; Chaotic synchronization; Neuron system

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In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response. Furthermore, the chaotic synchronization with a gap junction of two or multi-coupled-neurons of fractional-order are discussed. The circuit model, fractional-order state equations and the numerical technique are introduced in this paper for individual and multiple coupled neuron systems with different fractional-orders. Various examples are introduced with different fractional orders using the nonstandard finite difference scheme together with the Grunwald-Letnikov discretization process which is easily implemented and reliably accurate. (C) 2012 Elsevier Ltd. All rights reserved.

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