Infinite attractors in a chaotic circuit with exponential memristor and Josephson junction resonator

Abstract

Memristors play a vital role in the design of high density and low power memory devices. Considering the complex behaviour of memristor devices because of the feature that its memductance changes with the input current, these devices finds its applications in design of nonlinear circuits. Similarly, Josephson junction resonators also exhibit complex behaviours because of its inductive properties. To model the effect of magnetic flux effects on the Josephson junction devices, we introduce the memristor to produce the feedback effect between magnetic flux and junction potential. Such a circuit produce interesting complex behaviours and hence in this paper we propose a nonlinear chaotic oscillator in a memristor-Josephson junction combination. Due to the variation laws of the flux-controlled memductance, it will not always be the same when the excitation voltage changes and hence have their drawbacks in real word applications. Considering this, we use an exponential memristor which overcomes this problem and hence can be used in physical applications. By varying the type of the bias current, we could observe the property of megastability in the memristor-Josephson junction oscillator (when excited by an AC current), which was not been observed in real physical circuits. To show the applicational benefits of the proposed oscillator, we have discussed about the synchronisation of the master-slave memristor-Josephson junction oscillators and used it in secure communication systems.