Asymmetric Double Strange Attractors in a Simple Autonomous Jerk Circuit

G H Kom,G Kenne,A B Tiedeu,J R Mboupda Pone,J Kengne

doi:10.1155/2018/4658785

Abstract

The dynamics of a simple autonomous jerk circuit previously introduced by Sprott in 2011 are investigated. In this paper, the model is described by a three-time continuous dimensional autonomous system with an exponential nonlinearity. Using standard nonlinear techniques such as time series, bifurcation diagrams, Lyapunov exponent plots, and Poincaré sections, the dynamics of the system are characterized with respect to its parameters. Period-doubling bifurcations, periodic windows, and coexisting bifurcations are reported. As a major result of this work, it is found that the system experiences the unusual phenomenon of asymmetric bistability marked by the presence of two different attractors (e.g., screw-like Shilnikov attractor with a spiralling-like Feigenbaum attractor) for the same parameters setting, depending solely on the choice of initial states. Among few cases of lower dimensional systems capable of such type of behavior reported to date (e.g., Colpitts oscillator, Newton–Leipnik system, and hyperchaotic oscillator with gyrators), the jerk circuit/system considered in this work represents the simplest prototype. Results of theoretical analysis are perfectly reproduced by laboratory experimental measurements.

Highlights

The phenomenon of multistability has captivated the attention of most researchers in recent years
We consider the dynamics of an extremely simple chaotic jerk circuit recently introduced by Sprott [18] with particular attention on the chaos mechanism as well as the possibility of multiple coexisting attractors
Motivated by the outcomes we have mentioned above, this paper studies the dynamics of the simple jerk circuit previously introduced by Sprott [18] with the following key objectives: (a) to carry out a systematic analysis of the novel jerk circuit and explain the chaos mechanism; (b) to precise the region in parameter space, in which the proposed model exhibits multiple coexisting attractors and hysteretic dynamics; (c) to realize an experimental study of the system to support the theoretical predictions

Summary

Introduction

The phenomenon of multistability (i.e., the occurrence of multiple attractors for the same parameters setting depending solely on the choice of initial conditions) has captivated the attention of most researchers in recent years. We consider the dynamics of an extremely simple chaotic jerk circuit recently introduced by Sprott [18] with particular attention on the chaos mechanism as well as the possibility of multiple coexisting attractors. Motivated by the outcomes we have mentioned above, this paper studies the dynamics of the simple jerk circuit previously introduced by Sprott [18] with the following key objectives: (a) to carry out a systematic analysis of the novel jerk circuit and explain the chaos mechanism; (b) to precise the region in parameter space, in which the proposed model exhibits multiple coexisting attractors and hysteretic dynamics; (c) to realize an experimental study of the system to support the theoretical predictions.

Circuit Description and State Equation

Analysis of the Model

Numerical Study

Experimental Study

Concluding Remarks