Effects of initial conditions on the synchronization of the coupled memristor neural circuits

The fourth basic two-terminal circuit element has been called the memristor because its resistance (conductance) depends on the complete past history of the memristor current (voltage), i.e., the initial charge (flux) condition at a given instant. This paper aims to provide some insight into the effects of the initial flux condition of the memristor synapse in the synchronization of two coupled memristor-based neural circuits. First, we build the coupled memristor-based FitzHugh–Nagumo circuits with the memristor synapse, and obtain the initial conditions by means of the flux-charge analysis method in the differential equations. Then, as a result of varying the initial conditions of the coupling memristor in the neural network, the details of synchronization with the parallel shift are derived theoretically by solving the nonhomogeneous error equations. These results of theoretical analyses have been confirmed by numerical simulations. Finally, we focus on the influence of the initial condition of the memristor on chaos generation for individual FitzHugh–Nagumo neuron and how to change chaotic state into stable periodic oscillation for a FitzHugh–Nagumo neuron in the synchronous neural network.