Abstract
This paper generalizes the Izhikevich neuron model in the fractional-order domain for better modeling of neuron dynamics. Accurate and computationally efficient numerical techniques such as non-standard finite difference (NSFD) scheme is used to solve the neuron system in the fractional-order domain for different cases. Neuron synchronization plays an important role in the process of information exchange among coupled neurons. The general formula for the synchronization of different Izhikevich neurons is proposed. Also, the synchronization of two and three neurons are studied at different fractional orders. Furthermore, the fractional-order regular spiking neuron of Izhikevich model is implemented on Xilinx (XC5VLX30T) Virtex 5 FPGA kit using only combinational logic. FPGAs are known for their reconfigurability and parallelism which makes them suitable for large-scale neural network simulations.
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