Synchronization: a tool for validating a PWL circuit that approximates the Hindmarsh-Rose neuron model

This paper uses synchronization as a tool for further validating a circuit (HR-PWL circuit) recently proposed in the literature and based on a piecewise-linear (PWL) approximation of the Hindmarsh-Rose (HR) neuron model. The accuracy of the single neuron hardware implementation has been already validated through bifurcation analysis tools. Here, the synchronization behavior of networks formed by HR neurons is simulated and compared to that of companion networks of PWL neurons, with the purpose of validating the HR-PWL circuit also from a collective behavior point of view. In the considered cases, the neurons are connected either by linear diffusive or by nonlinear sigmoidal coupling, with different topologies. The analysis is based on the Master Stability Function approach and is verified by extensive numerical time-domain simulations. The synchronization properties of the PWL neuron networks turn out to be qualitatively very similar to those of the companion HR networks, confirming the validity of the proposed hardware-implemented neuron.