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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.

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Authors and Affiliations

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710072, China

    Lin Du, Yong Yang & Youming Lei

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  1. Lin Du
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  2. Yong Yang
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  3. Youming Lei
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Correspondence to Youming Lei.

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Citation: Du, L., Yang, Y., and Lei, Y. M. Synchronization in a fractional-order dynamic network with uncertain parameters using an adaptive control strategy. Applied Mathematics and Mechanics (English Edition), 39(3), 353–364 (2018) https://doi.org/10.1007/s10483-018-2304-9

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Du, L., Yang, Y. & Lei, Y. Synchronization in a fractional-order dynamic network with uncertain parameters using an adaptive control strategy. Appl. Math. Mech.-Engl. Ed. 39, 353–364 (2018). https://doi.org/10.1007/s10483-018-2304-9

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  • DOI: https://doi.org/10.1007/s10483-018-2304-9

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

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