Bifurcations and Synchronization of the Fractional-Order Bloch System

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 cyc...

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Bibliographic Details
Published in:Discrete dynamics in nature and society 2017-01, Vol.2017 (2017), p.1-10
Main Authors: Yang, Li-xin, Dang, Honggang, Hong, Ling, Liu, Xiaojun
Format: Article
Language:English
Subjects:
Algorithms
Bifurcation theory
Bifurcations
Calculus
Chaos synchronization
Control theory
Controllers
Dynamical systems
Dynamics
Eigenvalues
Mathematical models
Mathematical research
Ordinary differential equations
Parameters
Simulation
Synchronism
Synchronization
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Summary: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.
ISSN:1026-0226
1607-887X
DOI:10.1155/2017/4694305