Second Order Memristor Models for Neuromorphic Computing

Second order memristors 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 to implement locally competitive algorithms (LCA) and to tackle classification problems, by exploiting temporal learning techniques. On the other hand neuromorphic studies and experiments have revealed different kinds of plasticity and have shown the effect of calcium concentration on synaptic changes. In this paper we firstly derive a simplified model of a second order memristor, only involving two variables, the mem-conductance and the temperature, directly ascribable to the synaptic efficacy and to the calcium concentration. Then we provide a comparison between second order memristors and neuromorphic models, with reference to some relevant plasticity models, including cycles of spike pairs, triplets and quadruplets at different frequencies. Preliminary results show that, through our almost analytical approach, a significant portion of synaptic behaviors in second order memristors can be easily studied and predicted.