Correlation Between the Theory of Lissajous Figures and the Generation of Pinched Hysteresis Loops in Nonlinear Circuits

In this paper, the application of the theory of Lissajous figures to the creation of pinched hysteresis loops, considered to be a characteristic of memristive systems, is demonstrated and experimentally verified using designed electronic circuits in the form of an input impedance. The relationship between the Lissajous-based model of the pinched hysteresis loop and a previously reported integrator-multiplier model is clarified. Important special cases are highlighted and necessary conditions to obtain a pinch point, loops with positive or negative inclination, as well as no pinch point are given. We show that in devices (memristors or other devices) and circuits which exhibit this behavior, a nonlinearity that performs the necessary frequency doubling mandated by the theory must exist.