About this Journal Submit a Manuscript Table of Contents
International Journal of Differential Equations
Volume 2012 (2012), Article ID 623234, 16 pages
http://dx.doi.org/10.1155/2012/623234
Research Article

Chaos Control and Synchronization in Fractional-Order Lorenz-Like System

Department of Mathematics, Shivaji University, Vidyanagar, Kolhapur 416004, India

Received 6 May 2012; Accepted 22 June 2012

Academic Editor: Wen Chen

Copyright © 2012 Sachin Bhalekar. 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 present paper deals with fractional-order version of a dynamical system introduced by Chongxin et al. (2006). The chaotic behavior of the system is studied using analytic and numerical methods. The minimum effective dimension is identified for chaos to exist. The chaos in the proposed system is controlled using simple linear feedback controller. We design a controller to place the eigenvalues of the system Jacobian in a stable region. The effectiveness of the controller in eliminating the chaotic behavior from the state trajectories is also demonstrated using numerical simulations. Furthermore, we synchronize the system using nonlinear feedback.