Synchronization properties in networks of Hindmarsh-Rose neurons and their PWL approximations with linear symmetric coupling

In this paper we analyze the collective behaviors of networks of Hindmarsh-Rose (HR) neurons and compare them with the behaviors of networks of piecewise-linear (PWL) approximations of the HR neurons. In all cases, the neurons are assumed to be symmetrically and diffusively coupled, with different topologies. The analysis is based on the Master Stability Function (MSF) approach. The obtained results are verified by numerical time domain simulations of networks of 100 neurons. The synchronization properties of the PWL networks turn out to be very similar to those of the HR networks, as well as the dynamical properties of the single neurons (analyzed elsewhere).