非自治复合系统的集态敏感性和集态可达性  

The Collectively Sensitivity and Accessible in Non-Autonomous Composite Systems

作　　者：杨晓芳 唐孝 卢天秀 Yang Xiaofang;Tang Xiao;Lu Tianxiu(College of Mathematics and Statistics,Sichuan University of Science and Engineering,Sichuan Zigong 643000;School of Mathematical Science,Sichuan Normal University,Chengdu 610068;Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things,Sichuan Zigong 643000)

机构地区：[1]四川轻化工大学数学与统计学院,四川自贡643000 [2]四川师范大学数学科学学院,成都610068 [3]企业信息化与物联网测控技术四川省高校重点实验室,四川自贡643000

出　　处：《数学物理学报（A辑）》2021年第5期1545-1554,共10页Acta Mathematica Scientia

基　　金：四川省科技计划(19YYJC2845);企业信息化与物联网测控技术四川省高校重点实验室开放基金(2020WZJ01);四川轻化工大学人才引进项目(2020RC24);研究生创新基金项目(Y2020077)。

摘　　要：该文在非自治离散系统中定义了集态敏感,集态无限敏感,集态Li-Yorke敏感和集态可达.首先,证明了紧度量空间上映射序列(f_(k))k=1∞是p-混沌的当且仅当■n∈N(N是自然数集且不含0),映射序列(f_(k))k=n∞是p-混沌的.然后,在f_(1,∞)一致收敛的条件下,证明了f_(1,∞)具有CP-混沌性当且仅当复合系统f_(1,∞)[m](m∈N)也具有CP-混沌性.其中,P-混沌表示下面五个性质之一:传递性、敏感性、无限敏感性、可达性和正合性;CP-混沌性表示下面圆个性质之一:集态敏感性,集态无限敏感性,集态Li-Yorke敏感性和集态可达性.In this paper,collectively sensitivity,collectively infinity sensitivity,collectively LiYorke sensitivity and collectively accessible are defined in the non-autonomous discrete system.First of all,it is showed that,on compact metric spaces,mapping sequence(fk)k=1∞is P-chaos if and only if■n∈N(N is the set of natural numbers and does not contain 0).Then,under the condition that f1,∞is uniformly convergence,it is proved that f1,∞is CP-chaos if and only if for any m∈N,f1,∞[m]is CP-chaos.Where P-chaos denote one of the five properties:transitivity,sensitivity,infinitely sensitivity,accessibility and exact,CP-chaos denote one of the four properties:collectively sensitivity,collectively infinity sensitivity,collectively Li-Yorke sensitivity and collectively accessible.

关 键 词：非自治离散系统 复合映射 传递性 敏感性 可达性 

分 类 号：O193[理学—数学]