Edge-Based Fractional-Order Adaptive Strategies for Synchronization of Fractional-Order Coupled Networks With Reaction-Diffusion Terms

In this paper, spatial diffusions are introduced to fractional-order coupled networks and the problem of synchronization is investigated for fractional-order coupled neural networks with reaction-diffusion terms. First, a new fractional-order inequality is established based on the Caputo partial fra...

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Bibliographic Details
Published in:IEEE transactions on cybernetics 2020-04, Vol.50 (4), p.1582-1594
Main Authors: Lv, Yujiao, Hu, Cheng, Yu, Juan, Jiang, Haijun, Huang, Tingwen
Format: Article
Language:English
Subjects:
Adaptive control
Biological neural networks
Complex networks
Computer simulation
Coupled neural network
Coupling
Couplings
edge-based adaptive law
fractional-order
Neural networks
reaction-diffusion
Synchronism
Synchronization
Time dependence
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Summary:In this paper, spatial diffusions are introduced to fractional-order coupled networks and the problem of synchronization is investigated for fractional-order coupled neural networks with reaction-diffusion terms. First, a new fractional-order inequality is established based on the Caputo partial fractional derivative. To realize asymptotical synchronization, two types of adaptive coupling weights are considered, namely: 1) coupling weights only related to time and 2) coupling weights dependent on both time and space. For each type of coupling weights, based on local information of the node's dynamics, an edge-based fractional-order adaptive law and an edge-based fractional-order pinning adaptive scheme are proposed. Furthermore, some new analytical tools, including the method of contradiction, L'Hopital rule, and Barbalat lemma are developed to establish adaptive synchronization criteria of the addressed networks. Finally, an example with numerical simulations is provided to illustrate the validity and effectiveness of the theoretical results.
ISSN:2168-2267
2168-2275
DOI:10.1109/TCYB.2018.2879935