A physical memristor based Muthuswamy-Chua-Ginoux system

TL;DR

This paper introduces a physical memristor-based chaotic circuit using a thermistor, demonstrating a transition from torus breakdown to chaos with a unique double spiral attractor, advancing understanding of memristor dynamics.

Contribution

It presents the first implementation of a physical memristor in a Muthuswamy-Chua system, revealing novel chaotic behaviors and a new route to spiral chaos.

Findings

Transition from torus breakdown to chaos observed.

Identification of a double spiral attractor.

Mathematical analysis confirms route to Shilnikov spiral chaos.

Abstract

In 1976, Leon Chua showed that a thermistor can be modeled as a memristive device. Starting from this statement we designed a circuit that has four circuit elements: a linear passive inductor, a linear passive capacitor, a nonlinear resistor and a thermistor, that is, a nonlinear "locally active" memristor. Thus, the purpose of this work was to use a physical memristor, the thermistor, in a Muthuswamy-Chua chaotic system (circuit) instead of memristor emulators. Such circuit has been modeled by a new three-dimensional autonomous dynamical system exhibiting very particular properties such as the transition from torus breakdown to chaos. Then, mathematical analysis and detailed numerical investigations have enabled to establish that such a transition corresponds to the so-called route to Shilnikov spiral chaos but gives rise to a "double spiral attractor".