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

doi:10.1088/1674-1056/23/8/080206

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.

Keywords: FitzHugh-Nagumo system graph stabilization internal controller

Received: 28 October 2013
Revised: 27 November 2013
Accepted manuscript online:

PACS:	02.30.Yy	(Control theory)
	89.75.-k	(Complex systems)
	87.10.Ed	(Ordinary differential equations (ODE), partial differential equations (PDE), integrodifferential models)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61374096, 61104048, and 11231007) and the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6110751).

Corresponding Authors: Xu Chao
E-mail: cxu@zju.edu.cn

Cite this article:

Yu Xin (于欣), Xu Chao (许超), Lin Qun (林群) A feedback control method for the stabilization of a nonlinear diffusion system on a graph 2014 Chin. Phys. B 23 080206

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