Table of Contents
Journal of Chaos
Volume 2013, Article ID 839038, 12 pages
Research Article

Dynamical Properties and Finite-Time Hybrid Projective Synchronization Using Fractional Nonsingular Sliding Mode Surface in Fractional-Order Two-Stage Colpitts Oscillators

1Laboratory of Electronics and of Signal Processing, Department of Physics, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon
2Research Group on Experimental and Applied Physics for Sustainable Development (EAPhySuD), P.O. Box 412, Dschang, Cameroon
3Laboratoire de Mécanique et de Modélisation des Systèmes, Département de Physique, Faculté des Sciences, Université de Dschang, B.P. 67, Dschang, Cameroon

Received 30 August 2013; Accepted 28 October 2013

Academic Editor: Uchechukwu E. Vincent

Copyright © 2013 Romanic 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.


The dynamics and robust finite-time hybrid projective synchronization of a fractional-order four-dimensional nonlinear system based on a two-stage Colpitts oscillator is investigated. The study of the fractional order stability of the equilibrium states of the system is carried out. The bifurcation diagram confirms the occurrence of Hopf bifurcation in the proposed system when the fractional-order passes a sequence of critical values; the Lyapunov exponent shows the different chaotic sequences of the system. Further, a fractional nonsingular terminal sliding surface and an appropriate robust fractional sliding mode control law are proposed for the finite-time hybrid projective synchronization of a fractional-order chaotic two-stage Colpitts oscillator by taking into account the effects of model uncertainties and the external disturbances. The fractional version of the Lyapunov stability is used to prove the finite-time existence of the sliding motion. Finally, some numerical simulations are presented to demonstrate the effectiveness and applicability of the proposed technique.