Simulations of Memristors Using the Poincaré Map Approach

In many memristor models the internal variable is related to the width of a conductive layer and is therefore limited by the physical dimensions of the device. The necessity of keeping the internal variable within allowable limits may introduce discontinuities in right hand sides of differential equations describing dynamics of circuits with memristors. Such discontinuities are difficult to handle using standard numerical integration methods. An approach based on the concept of a Poincaré map is proposed to solve these difficulties. Two examples are discussed to show the usefulness of the proposed technique.