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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2019, Vol. 36 ›› Issue (1): 115-122.doi: 10.3969/j.issn.1005-3085.2019.01.010

• • 上一篇    

模糊动力系统的等度连续和 Distal 模糊动力系统（英）

陆汉川1,  伏文清2,  李生刚3   

  1. 1- 贵州大学数学与统计学院，贵阳  550025
    2- 西安工业大学理学院，西安  710021
    3- 陕西师范大学数学与信息科学学院，西安  710062
  • 收稿日期:2017-03-28 接受日期:2018-09-05 出版日期:2019-02-15 发布日期:2019-04-15
  • 基金资助:
    国家自然科学基金(11071151)；中国国际科技合作基金会(2012DFA11270).

Equicontinuous of Fuzzy Dynamical Systems and Distal Fuzzy Dynamic System

LU Han-chuan1,  FU Wen-qing2,  LI Sheng-gang3   

  1. 1- School of Mathematics and Statistics, Guizhou University, Guiyang 550025 
    2- College of Science, Xi'an Technological University, Xi'an 710021 
    3- College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062
  • Received:2017-03-28 Accepted:2018-09-05 Online:2019-02-15 Published:2019-04-15
  • Supported by:
    The National Natural Science Foundation of China (11071151); the International Science and Technology Cooperation Foundation of China (2012DFA11270).

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摘要： 等度连续性具有很强的稳定性，只要系统初始状态的误差足够小，那么其运动的未来状态可以确保在预先给定的误差范围内．等度连续性所揭示的这一动力行为在应用上有很高的应用价值．因此，在微分方程稳定性理论和拓扑动力系统中有着重要的研究价值．而等度连续和 distal 与混沌等有着密切的联系，为了在模糊的背景下研究它们．我们利用一般化的方法，通过建立模糊动力系统，给出了模糊动力系统等度连续的定义，得到了下面的一些结果：1) 模糊动力系统等度连续的等价命题；2) 等度连续在模糊一致拓扑共轭下的保持性；3) 两个模糊动力系统同 distal 的充分必要条件．

关键词: 标准的模糊度量空间, 模糊动力系统, 等度连续, 模糊一致拓扑共轭, distal

Abstract: The equicontinuity has strong stability, it can be ensured within a pre-given error range if the error of its initial state is small enough. This dynamic behavior revealed by equicontinuity has high application value. Therefore, it has important research value in the theory of differential equation stability and topological dynamic system. Equicontinuity and distal are closely related to chaos and so on. In order to study them under the background of fuzzyness, a method of generalization is used to give the definition of the equicontinuity in fuzzy dynamic systems with establishing of fuzzy dynamic system. The following results were obtained: 1)~Equivalent propositions of the equicontinuity in fuzzy dynamic system; 2)~The equicontinuity is preserved under fuzzy uniform topologically conjugate mapping; 3)~The sufficient and necessary condition of two fuzzy dynamical systems to be distal.

Key words: standard fuzzy metric space, fuzzy dynamical system, equicontinuity, fuzzy uniform topologically conjugate, distal

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