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The Scientific World Journal
Volume 2013, Article ID 645080, 13 pages
http://dx.doi.org/10.1155/2013/645080
Research Article

Stability Analysis of Distributed Order Fractional Chen System

1Department of Applied Mathematics, School of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran
2Department of Applied Mathematics, Faculty of Mathematical Sciences, Islamic Azad University, Lahijan Branch, P.O. Box 1616, Lahijan, Iran

Received 31 August 2013; Accepted 3 October 2013

Academic Editors: C. Li, F. Liu, and R. Magin

Copyright © 2013 H. Aminikhah 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

We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results.