Dynamical behaviors of a chaotic jerk circuit based on a novel memristive diode emulator with a smooth symmetry control

Abstract

This paper presents a new chaotic memristive circuit, which is derived from the autonomous jerk circuit by replacing the first-order generalized memristive diode bridge with a simple second-order memristive emulator, which consists of six elementary electronic elements. This second-order memristive emulator model addresses the problem of changing the configuration of the diode-bridge memristor model when used for symmetry control of chaotic systems. It also allows to reduce the gap between the experimental and the numerical simulations in that during the experimental, the symmetry breaking is done by a discrete modification of the number of diodes on the branches of the diode bridge, whereas during the numerical simulations, the variation of the symmetry control parameter corresponding to the number of diodes is continuous. Thus, a new memristor emulator consisting of two diodes, two resistors and two capacitors is developed and proposes a method of control by continuous variations of a potentiometer to perform symmetry breaking. Using tools for characterizing dynamic systems such as bifurcation diagrams, Lyapunov spectrum and phase portraits, to name just a few, it is shown how the new memristive emulator model can be used to check symmetry. The first major contribution of this work is the control of the symmetry of a jerk oscillator when the resistors of the memristive emulator take different values without modifying its structure. The second major contribution of this work is the ability to change the nature of an attractor as a function of its position in phase space without changing the nature of its associated symmetric attractor, which is demonstrated using phase portraits and initial condition diagrams. An electronic circuit is presented showing how symmetry control is achieved by varying a potentiometer. And an experimental study is performed to validate the results.