Memristor Circuits: Pulse Programming via Invariant Manifolds

This paper considers a large class of memristor circuits of arbitrary order, and containing an arbitrary number of flux- or charge-controlled memristors, for which a state equation (SE) description can be obtained. By means of the SEs, it is shown that the state space of each circuit can be decomposed in infinitely many manifolds, and that in the autonomous case, each manifold is positively invariant and is characterized by a different reduced-order dynamics and attractors. These results are the basis for extending the analysis to the non-autonomous case, where time-varying independent sources are present. In particular, the chief result obtained in this paper shows how to analytically design external pulses for programming memristor circuits, i.e., how invariant manifolds and attractors can be changed and controlled by applying suitable charge or flux sources via time-varying voltage and/or current pulses with finite time duration. The main results are obtained by relying on a recently introduced technique for the analysis of memristor circuits in the flux-charge domain.