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;

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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