Abstract
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 non-standard finite difference scheme together with the Grünwald-Letnikov discretization process which is easily implemented and reliably accurate. © 2011 Elsevier Ltd. All rights reserved.
Original language | English (US) |
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Pages (from-to) | 3329-3339 |
Number of pages | 11 |
Journal | Computers & Mathematics with Applications |
Volume | 64 |
Issue number | 10 |
DOIs | |
State | Published - Nov 2012 |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01ASJC Scopus subject areas
- Modeling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics