Pattern Characterization in Second Order Memristor Networks

Second order memristors are two terminal devices which present a conductance depending on two orders of variables, namely the geometric parameters and the internal temperature. They have shown to be able to mimic some specific features of neuron synapses, specifically Spike-Timing-Dependent-Plasticity (STDP), and consequently to be good candidates for neuromorphic computing. In particular memristor crossbar structures appear to be suitable for implementing locally competitive algorithms and for tackling classification problems, by exploiting temporal learning techniques. On the other hand spiking networks have been intensively studied in the context of unsupervised, supervised and reinforcement learning. In this manuscript we briefly present a simplified model of second order memristors, that we have derived in a previous paper. Then we focus on two main results. As a first step we show that the model is capable of accurately reproducing a correct synaptic response to complex inputs, like cycles of spike triplets and quadruplets at different frequencies. Then we show that, exploiting such a simple model, complex spatio-temporal patterns can be almost analytically characterized, in memristor networks connecting an arbitrary number of presynaptic and postsynaptic neurons.