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The fractional-order modeling and synchronization of electrically coupled neuron systems. (English) Zbl 1268.92026
Summary: 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 Grünwald-Letnikov discretization process, which is easily implemented and reliably accurate.

MSC:
92C20Neural biology
34A08Fractional differential equations
34D06Synchronization
65L06Multistep, Runge-Kutta, and extrapolation methods
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References:
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