PWL approximation of the Hindmarsh-Rose neuron model in view of its circuit implementation

Abstract

A two-dimensional piecewise-linear approximation of the Hindmarsh-Rose neuron model is obtained, in view of its circuit implementation. The obtained approximation is checked by varying two bifurcation parameters. The brute-force two-dimensional bifurcation diagram of the original model is compared with the one of the piecewise-linear approximation, showing that the approximation is able to reproduce the main qualitative behaviours (quiescency, spiking, bursting, chaotic dynamics) of the original model.