Table of Contents
Journal of Nonlinear Dynamics
Volume 2014, Article ID 815783, 13 pages
http://dx.doi.org/10.1155/2014/815783
Research Article

Experiment on Bifurcation and Chaos in Coupled Anisochronous Self-Excited Systems: Case of Two Coupled van der Pol-Duffing Oscillators

1Laboratory of Automation and Applied Computer (LAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, P.O. Box 134, Bandjoun, Cameroon
2Institute for Smart-Systems Technologies, University of Klagenfurt, Universitätsstraße 65, 9020 Klagenfurt, Austria
3Department of Physics, University of Yaoundé 1, P.O. Box 8390, Yaoundé, Cameroon
4Laboratory of Electronics, Department of Physics, University of Dschang, P.O. Box 134, Bandjoun, Cameroon

Received 29 June 2014; Revised 17 September 2014; Accepted 19 September 2014; Published 29 October 2014

Academic Editor: Mohamed Belhaq

Copyright © 2014 J. Kengne 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 analog circuit implementation and the experimental bifurcation analysis of coupled anisochronous self-driven systems modelled by two mutually coupled van der Pol-Duffing oscillators are considered. The coupling between the two oscillators is set in a symmetrical way that linearly depends on the difference of their velocities (i.e., dissipative coupling). Interest in this problem does not decrease because of its significance and possible application in the analysis of different, biological, chemical, and electrical systems (e.g., coupled van der Pol-Duffing electrical system). Regions of quenching behavior as well as conditions for the appearance of Hopf bifurcations are analytically defined. The scenarios/routes to chaos are studied with particular emphasis on the effects of cubic nonlinearity (that is responsible for anisochronism of small oscillations). When monitoring the control parameter, various striking dynamic behaviors are found including period-doubling, symmetry-breaking, multistability, and chaos. An appropriate electronic circuit describing the coupled oscillator is designed and used for the investigations. Experimental results that are consistent with results from theoretical analyses are presented and convincingly show quenching phenomenon as well as bifurcation and chaos.