| Summary: | Memristors (abbreviation of memory and resistor), introduced as the fourth fundamental electrical circuit element, remember the electric charge that flowed through it. These nonlinear elements are considered as a class of two terminal resistive devices and offers a lot of possible applications in various areas. In this article, we review the dynamical behaviour of some electrical circuits with memristors. Initially, we show that a simple circuit with a capacitor and an inductor connected to a memristor exhibits periodic and chaotic attractors. After that, we show that the known Chua circuit, with a nonlinear resistance, can generate bifurcations and chaos. Substituting the nonlinear resistance by a memristor, the modified Chua circuit exhibits coexistence of attractors. Another known circuit, the Colpitts, is made of a combination of capacitors and inductors containing a bipolar junction transistor. We show that the modified Colpitts circuit, created by substituting the transistor by a memristor, presents multistability and coexistence of many attractors.
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