Synchronization of memristor based bidirectionally coupled Hindmarsh-Rose neurons

Abstract

An ideal memristor is a device whose resistive memory value is determine by its initial conditions and the voltage that has been applied across its terminals. As such, it is a good candidate to model the synaptic plasticity of neural systems. When memristors are included in neural models, they are called memristive neural networks. In this contribution, we investigate the emergence of synchronization in an array of two identical Hindmarsh-Rose neurons bidirectionally coupled through their voltage variables via memristors. We show that, for a sufficiently large positive memductance, synchronization emerges between neurons while the memristors converge to constant synaptic weight values. We illustrate our results with numerical simulations.