Synchronization and Anti-synchronization of Coupled Hindmarsh–Rose Neuron Models

In this paper, a coupling scheme based on Nonlinear Open Loop Controllers, between two identical coupled Hindmarsh–Rose neuron models is investigated analytically and numerically. In more details the cases of bidirectional and unidirectional coupling are chosen, which are designed for achieving two of the more interesting types of synchronization the complete synchronization and anti-synchronization. The stability of the proposed method is ensured by using the Lyapunov function stability theory. Simulation results verified that the proposed coupling scheme drives the system either to complete synchronization or anti-synchronization depending on the choice of the signs of the error function’s parameters. Furthermore, the Hindmarsh–Rose neuron model is emulated by an electronic circuit and its dynamical behavior is studied by using the electronic simulation package Cadence OrCAD in order to confirm the feasibility of the theoretical model.