Table of Contents
Journal of Nonlinear Dynamics
Volume 2017, Article ID 5483956, 13 pages
Research Article

Complex Dynamics and Synchronization in a System of Magnetically Coupled Colpitts Oscillators

1Laboratory of Electronics and Signal Processing, Department of Physics, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon
2Department of Physics, Faculty of Science, University of Douala, P.O. Box 24157, Douala, Cameroon
3Laboratory of Mechanics and Modeling of Physical Systems, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon

Correspondence should be addressed to L. K. Kana; moc.oohay@lkgnagmek

Received 8 October 2016; Revised 13 February 2017; Accepted 23 February 2017; Published 10 April 2017

Academic Editor: Zhao Lu

Copyright © 2017 L. K. Kana 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.


We propose the use of a simple, cheap, and easy technique for the study of dynamic and synchronization of the coupled systems: effects of the magnetic coupling on the dynamics and of synchronization of two Colpitts oscillators (wireless interaction). We derive a smooth mathematical model to describe the dynamic system. The stability of the equilibrium states is investigated. The coupled system exhibits spectral characteristics such as chaos and hyperchaos in some parameter ranges of the coupling. The numerical exploration of the dynamics system reveals various bifurcations scenarios including period-doubling and interior crisis transitions to chaos. Moreover, various interesting dynamical phenomena such as transient chaos, coexistence of solution, and multistability (hysteresis) are observed when the magnetic coupling factor varies. Theoretical reasons for such phenomena are provided and experimentally confirmed with practical measurements in a wireless transfer.