EXPLICIT ODE REDUCTION OF MEMRISTIVE SYSTEMS

Abstract

The recent discovery of a physical device behaving as a memristor has driven a lot of attention to memristive systems, which are likely to play a relevant role in electronics in the near future, especially at the nanometer scale. The derivation of explicit ODE models for these systems is important because it opens a way for the study of the dynamics of general memristive circuits, including e.g. stability aspects, oscillations, bifurcations or chaotic phenomena. We tackle this problem as a reduction of implicit ODE (differential-algebraic) models, and show how tree-based approaches can be adapted in order to accommodate memristors. Specifically, we prove that the derivation of a tree-based explicit ODE model is feasible for strictly passive memristive systems under broad coupling effects and without a priori current/voltage control assumptions on tree/cotree elements. Our framework applies in particular to topologically degenerate circuits and accommodates a wide class of controlled sources. We also discuss a quasilinear reduction of nonpassive problems, which do not admit an explicit ODE description in the presence of singularities; some related bifurcations are addressed in this context.