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Complexity
Volume 2018 (2018), Article ID 4658785, 16 pages
https://doi.org/10.1155/2018/4658785
Research Article

Asymmetric Double Strange Attractors in a Simple Autonomous Jerk Circuit

1Laboratoire d’Automatique et Informatique Appliquée (LAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, P.O. Box 134, Bandjoun, Cameroon
2Groupe de Recherche sur les Technologies Médicales Adaptées aux Tropiques (GRETMAT), Laboratoire d’Electronique et de Traitement du Signal (LETS), ENSP, University of Yaoundé I, P.O. Box 8390, Yaounde, Cameroon

Correspondence should be addressed to G. H. Kom

Received 19 June 2017; Accepted 17 August 2017; Published 8 February 2018

Academic Editor: Mohamed Belhaq

Copyright © 2018 G. H. Kom et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.