Synchronization conditions in simple memristor neural networks

This paper aims to provide some insight into the mechanisms underlying the emergence of synchronization between two memristor-coupled Hindmarsh-Rose oscillatory neural cells. Extensive numerical investigations show that in some cases the history of the nonlinear dynamics of the memristor plays a key role in the development of synchronous oscillations in the network. In fact, an equivalent diffusive network, lacking the plasticity properties featured by the memristor-based synaptic coupling, fails to lock into synchronization under the same simulation settings. These results are then confirmed by a deep theoretical analysis based on the contraction mapping theory. This work sheds light on some aspects of the nonlinear behavior of the still largely unexplored memristor, which is doomed to make a revolutionary impact in integrated circuit design in the years to come.