Memristors and Bernoulli dynamics

This paper introduces a novel theoretical framework suitable for the study of memristors. The articulation of the framework relies upon the identification of a certain type of dynamics which comply with Bernoulli's differential equation and are thus termed Bernoulli dynamics. The paper explains how the Bernoulli dynamics: a) govern the dynamic behaviour of the ideal Williams memristors and other memelements, and b) how they can be exploited for the derivation and subsequent study of analytic expressions of the form I_mres = f(V_mres) or V_mres = g(I_mres) which define the relation between the memristor current I_mres and the memristor voltage V_mres Implications of the adoption of the new theoretical framework for future memristor-based circuit research are also discussed.