Behavioral Modeling of Memristors under Harmonic Excitation

Abstract

Memristors are devices built on the basis of fourth passive electrical elements in nanosystems. Because of the multitude of technologies used for memristor implementation, it is not always possible to obtain analytical models of memristors. This difficulty can be overcome using behavioral modeling, which is when mathematical models are constructed according to the input–output relationships on the input and output signals. For memristor modeling, piecewise neural and polynomial models with split signals are proposed. At harmonic input signals of memristors, this study suggests that split signals should be formed using a delay line. This method produces the minimum number of split signals and, as a result, simplifies behavioral models. Simplicity helps reduce the dimension of the nonlinear approximation problem solved in behavioral modeling. Based on the proposed method, the piecewise neural and polynomial models with harmonic input signals were constructed to approximate the transfer characteristic of the memristor, in which the current dynamics are described using the Bernoulli differential equation. It is shown that the piecewise neural model based on the feedforward network ensures higher modeling accuracy at almost the same complexity as the piecewise polynomial model.