Voltage-Current Differential Equations of Extended Memristors with One-Dimensional State

Abstract

The extended memristor is characterized by its port equation as state-dependent Ohm's law and by the state equation describing its dynamics. Its equivalent model is the differential equation (DE) between the memristor voltage, current, and their derivatives with respect to time. The paper presents the derivation of a general form of the DE for arbitrary extended memristors with scalar, i.e.one-dimensional state. It is shown that this DE is always a first-order nonlinear equation. DEs for the hyperbolic model of the Hewlett-Packard memristor with the Joglekar window function and also for some representatives of generic memristors are presented.