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    A feedback control method for the stabilization of a nonlinear diffusion system on the graph

    Access Status
    Fulltext not available
    Authors
    Yu, X.
    Xu, C.
    Lin, Qun
    Date
    2014
    Type
    Journal Article
    
    Metadata
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    Citation
    Yu, X. and Xu, C. and Lin, Q. 2014. A feedback control method for the stabilization of a nonlinear diffusion system on the graph. Chinese Physics B. 23 (8): pp. 080206-1-080206-6.
    Source Title
    Chinese Physics B
    DOI
    10.1088/1674-1056/23/8/080206
    ISSN
    1674-1056
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/43432
    Collection
    • Curtin Research Publications
    Abstract

    In this paper, we consider the internal stabilization problems of FitzHugh–Nagumo (FHN) systems on the locally finite connected weighted graphs, which describe the process of signal transmission across axons in neurobiology. We will establish the proper condition on the weighted Dirichlet–Laplace operator on a graph such that the nonlinear FHN system can be stabilized exponentially and globally only using internal actuation over a sub-domain with a linear feedback form.

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