Synchronization of Memristive Hindmarsh-Rose Neurons Connected by Memristive Synapses

We investigate the dynamics of a memristive Hindmarsh-Rose neuron model where an ideal memristor is used to add an additional electric current to the voltage membrane variable. For this memristive neuron model, we use local analysis to determine conditions for the emergence of different pattern of action potentials. Then, a flux-controlled memristor with a hyperbolic tangent memductance function is used to connect two of these models; for this arrangement, we investigate the emergence of identical synchronization throughout a normalized average synchronization error analysis. In this context, we explore two possible scenarios: in the first, two identical neurons under the same external excitation are coupled together, and in the second, the neurons are under different excitation (i.e., different external current inputs). In both scenarios, we identify a large set of coupling values such that synchronization is achieved by the memristor synapses even when the original trajectories of the neurons are markedly different.