The fractional-order modeling and synchronization of electrically coupled neuron systems
KAUST DepartmentElectrical Engineering Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Physical Sciences and Engineering (PSE) Division
Permanent link to this recordhttp://hdl.handle.net/10754/562390
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AbstractIn 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.