Chinese Quarterly Journal of Mathematics ›› 2020, Vol. 35 ›› Issue (3): 255-277.doi: 10.13371/j.cnki.chin.q.j.m.2020.03.002

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

  

  1. 1. School of Mathematics and Computational Science, Xiangtan University2. Department of Basic Education, Shangqiu Institute of Technology3. Xiangtan Industry and Trade School
  • Received:2018-10-13 Online:2020-09-30 Published:2020-10-22
  • About author: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.
  • Supported by:
    Supported by The Scientific Research Foundation Funded by Hunan Provincial Education Department under grant 19A503； Partially supported by Hunan Provincial Exploration of Undergraduate Research Learning and Innovative Experiment Project2018XTUSJ008； 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 lσ2×lσ2. We prove the existence and uniqueness of the solution to the lattice dynamical system FitzHugh-Nagumo in lσ2×lσ2. 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. 

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