模糊动力系统的等度连续和Distal模糊动力系统（英文）  

Equicontinuous of Fuzzy Dynamical Systems and Distal Fuzzy Dynamic System

作　　者：陆汉川 伏文清[2] 李生刚[3] LU Han-chuan;FU Wen-qing;LI Sheng-gang(School of Mathematics and Statistics, Guizhou University, Guiyang 550025;College of Science, Xi'an Technological University, Xi'an 710021;College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062)

机构地区：[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

出　　处：《工程数学学报》2019年第1期115-122,共8页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(11071151);the International Science and Technology Cooperation Foundation of China(2012DFA11270)

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.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.

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 

分 类 号：O189.13[理学—数学]