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Discrete Dynamics in Nature and Society
Volume 2018, Article ID 8284121, 10 pages
Research Article

Dynamics Analysis and Control of a Five-Term Fractional-Order System

1School of Arts and Sciences, Shaanxi University of Science and Technology, Xi’an 710021, China
2School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China

Correspondence should be addressed to Li-xin Yang; moc.361@nixilgnayadoaij

Received 31 May 2018; Revised 22 July 2018; Accepted 10 September 2018; Published 9 October 2018

Guest Editor: Abdul Qadeer Khan

Copyright © 2018 Li-xin Yang and Xiao-jun Liu. 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.


This paper proposes a new fractional-order chaotic system with five terms. Firstly, basic dynamical properties of the fractional-order system are investigated in terms of the stability of equilibrium points, Jacobian matrices theoretically. Furthermore, rich dynamics with interesting characteristics are demonstrated by phase portraits, bifurcation diagrams numerically. Besides, the control problem of the new fractional-order system is discussed via numerical simulations. Our results demonstrate that the new fractional-order system has compound structure.