Return Map Approach for Simulations of Electronic Circuits with Memristors

In this work, we discuss numerical methods for simulations of circuits containing memristors. In several models, the internal state of a memristor is limited by physical dimensions of the device. This introduces discontinuities in right hand sides of differential equations describing dynamics of circuits with memristors and makes it difficult to integrate such systems using standard numerical integration methods. An approach based on the concept of a return map is proposed to solve this problem. A simple example is discussed to show the usefulness of the proposed technique.