Mathematical models and circuit implementations of memristive systems

In this paper we first present a novel, simple and general boundary condition-based model for nano-scale switching resistances with memory. The boundary conditions are embedded into a switching function modulating the rate of ionic transport, and, on the basis of the memristor under modeling, may be suitably chosen through an optimization procedure minimizing some reference parameter such as the mean squared error between observed and modeled data. The versatile nature of the switching function enables the model to detect complex dynamics from a number of memristive nano-structures, including the Hewlett-Packard memristor. In the second part of the manuscript, we explain how to use the switching dynamics of appropriate nonlinear two-ports to synthesize simple memristive electronic circuits employing purely-passive already-existing components.