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Discrete Dynamics in Nature and Society
Volume 2016, Article ID 8712496, 13 pages
http://dx.doi.org/10.1155/2016/8712496
Research Article

Dynamic Analysis for a Fractional-Order Autonomous Chaotic System

1School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China
2School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China

Received 23 January 2016; Accepted 26 June 2016

Academic Editor: Viktor Avrutin

Copyright © 2016 Jiangang Zhang 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 introduce a discretization process to discretize a modified fractional-order optically injected semiconductor lasers model and investigate its dynamical behaviors. More precisely, a sufficient condition for the existence and uniqueness of the solution is obtained, and the necessary and sufficient conditions of stability of the discrete system are investigated. The results show that the system’s fractional parameter has an effect on the stability of the discrete system, and the system has rich dynamic characteristics such as Hopf bifurcation, attractor crisis, and chaotic attractors.