Global Attractor for High-dimensional SpaciallyDiscrete FitzHugh-Nagumo System in Weighted Space

YIN Fu-qi, JIANG Hong, JIN Meng-zhao, LIU Zhi-qi

doi:10.13371/j.cnki.chin.q.j.m.2020.02.005

Chinese Quarterly Journal of Mathematics >

0 188 - 209

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2020.02.005

Global Attractor for High-dimensional SpaciallyDiscrete FitzHugh-Nagumo System in Weighted Space

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1.School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China;
2.Department of Basic Education; Shangqiu Institute of Technology, Shangqiu 476000, China; 3.Xiang-tan Industry and Trade School, Xiangtan 411105, China

YIN Fu-qi(1970-), male, native of Xiangtan, Hunan, assistant professor of Xiangtan University, engages in in¯nite dynanmical system and stochastic dynanmical system; JIANG Hong(1990-), female, native of Fuyang, Anhui, a teacher of Shangqiu Institute of Technology,engages in ODE; JIN Meng-zhao(1996-),male,native of Luoyang, Henan, a undergraduate student of Xiangtan University, engages in mathematics and applied mathematics; LIU Zhi-qi(1973-), male, native of Xiangtan, Hunan, a associate professor of Xiangtan Industry and Trade School, engages in ODE.

Received date: 2017-06-27

Online published: 2020-09-03

Supported by

Supported by The Scienti¯c Research Foundation Funded by Hunan Provincial Educa tion Department under grant 19A503; Partially supported by Hunan Provincial Exploration of Undergraduate Research Learning and Innovative Experiment Project:2018XTUSJ008; Hunan Provincial Natural Science Foundation of China under grant 2015JJ2144.

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Abstract

In this paper, We study the global attractor and its properties on infinite lattice dynamical system FitzHugh-Nagumo in a weighted space $l_{\sigma}^2\times l_{\sigma}^2$. We prove the existence and uniqueness of the solution to the lattice dynamical system FitzHugh-Nagumo in $l_{\sigma}^2\times l_{\sigma}^2$. Then we get a bounded absorbing set, which suggests the existence of global attractors. Finally, we study the uniform boundedness and the upper semicontinuity of the global attractor.

Cite this article

YIN Fu-qi, JIANG Hong, JIN Meng-zhao, LIU Zhi-qi . Global Attractor for High-dimensional SpaciallyDiscrete FitzHugh-Nagumo System in Weighted Space[J]. Chinese Quarterly Journal of Mathematics, 0 : 188 -209 . DOI: 10.13371/j.cnki.chin.q.j.m.2020.02.005

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