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

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Abstract
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.
Funding Information
  • National Natural Science Foundation of China (61563048, 61866036, 11402223, U1703262)
  • Innovation Team Program of Universities in Xinjiang Uyghur Autonomous Region (XJEDU2017T001)
  • Natural Science Foundation of Xinjiang Uygur Autonomous Region (2018D01C057)
  • Qatar National Research Fund (NPRP8-274-2-107)

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