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Discrete Dynamics in Nature and Society
Volume 2017, Article ID 4694305, 10 pages
https://doi.org/10.1155/2017/4694305
Research Article

Bifurcations and Synchronization of the Fractional-Order Bloch System

1School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China
2State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Shaanxi, Xi’an 710049, China

Correspondence should be addressed to Xiaojun Liu; moc.621@2593ttebylf

Received 13 February 2017; Accepted 6 March 2017; Published 22 March 2017

Academic Editor: Mohamed A. Hajji

Copyright © 2017 Xiaojun Liu 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

In this paper, bifurcations and synchronization of a fractional-order Bloch system are studied. Firstly, the bifurcations with the variation of every order and the system parameter for the system are discussed. The rich dynamics in the fractional-order Bloch system including chaos, period, limit cycles, period-doubling, and tangent bifurcations are found. Furthermore, based on the stability theory of fractional-order systems, the adaptive synchronization for the system with unknown parameters is realized by designing appropriate controllers. Numerical simulations are carried out to demonstrate the effectiveness and flexibility of the controllers.