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Abstract and Applied Analysis
Volume 2015, Article ID 413540, 14 pages
http://dx.doi.org/10.1155/2015/413540
Research Article

Integer and Fractional General -System and Its Application to Control Chaos and Synchronization

West University of Timisoara, 4 Bulevardul Vasile Pârvan, 300115 Timisoara, Romania

Received 23 October 2014; Revised 26 March 2015; Accepted 1 April 2015

Academic Editor: Huang Xia

Copyright © 2015 Mihaela Neamţu 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 propose a three-dimensional autonomous nonlinear system, called the general system, which has potential applications in secure communications and the electronic circuit. For the general system with delayed feedback, regarding the delay as bifurcation parameter, we investigate the effect of the time delay on its dynamics. We determine conditions for the existence of the Hopf bifurcations and analyze their direction and stability. Also, the fractional order general -system is proposed and analyzed. We provide some numerical simulations, where the chaos attractor and the dynamics of the Lyapunov coefficients are taken into consideration. The effectiveness of the chaotic control and synchronization on schemes for the new fractional order chaotic system are verified by numerical simulations.