A dynamic system approach to spiking memristor network investigation

Second-order memristors are two-terminal devices that 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 accordingly to be good candidates for neuromorphic computing. Spiking memristor networks have been broadly investigated, mainly through extensive simulations in the context of unsupervised and supervised learning. In this manuscript, we study such networks from a different perspective by exploiting a recent developed almost-analytical model. We show that they can be accurately characterized as discrete nonlinear dynamical systems, with mem-conductances as state variables and pre and post-synaptic spikes as inputs and outputs, respectively. Under this approach, the network global dynamic behavior and the related learning mechanism can be deeply analyzed by employing advanced nonlinear dynamic techniques. As a preliminary result, we show that the network response to periodic presynaptic inputs can be readily determined by computing the system equilibrium points and discussing their stability properties.