Analysis and Design of Bio-Inspired Circuits with Locally-Active Memristors

As established by the second law of thermodynamics, an isolated system is unable to exhibit complex behaviours. Conversely, a physical system, which interacts with the surrounding environment, may support emergent phenomena, provided some of its constitutive components are capable to amplify infinitesimal fluctuations in energy under suitable polarization, a property which is referred to as Local Activity. Local Activity is in fact a New Universal Physics Principle, which, grounded on solid theoretical foundations, enables to explain emergent phenomena in any open system, e.g. the generation of All-or-None electrical spikes in neurons, and Symmetry-Breaking Effects in biological homogeneous cellular media. The existence of solid-state memristor nano-devices, which, similarly as the sodium and potassium ion channels, may operate in the Local Activity domain under opportune bias conditions, opens up new opportunities to synthesise circuits and systems, which, operating according to biological principles, may outperform traditional computing structures in terms of time and energy efficiency. This tutorial aims to shed light on the precious role that Nonlinear Circuit and System Theory shall assume in the years to come to support the exploration of the full potential of memristor physical realizations, which clearly show signs of Local Activity while admitting a Negative Differential Resistance upon suitable DC excitation, for bio-inspired electronics.