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Applied Mathematics and Mechanics

, Volume 39, Issue 3, pp 353–364 | Cite as

Synchronization in a fractional-order dynamic network with uncertain parameters using an adaptive control strategy

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Abstract

This paper studies synchronization of all nodes in a fractional-order complex dynamic network. An adaptive control strategy for synchronizing a dynamic network is proposed. Based on the Lyapunov stability theory, this paper shows that tracking errors of all nodes in a fractional-order complex network converge to zero. This simple yet practical scheme can be used in many networks such as small-world networks and scale-free networks. Unlike the existing methods which assume the coupling configuration among the nodes of the network with diffusivity, symmetry, balance, or irreducibility, in this case, these assumptions are unnecessary, and the proposed adaptive strategy is more feasible. Two examples are presented to illustrate effectiveness of the proposed method.

Keywords

fractional-order chaotic system synchronization complex dynamic network adaptive control 

Chinese Library Classification

O415.5 

2010 Mathematics Subject Classification

93C83 93D05 

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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied MathematicsNorthwestern Polytechnical UniversityXi’anChina

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