非自治复合系统的集态敏感性和集态可达性

数学物理学报 ›› 2021, Vol. 41 ›› Issue (5): 1545-1554.

非自治复合系统的集态敏感性和集态可达性

杨晓芳¹(),唐孝²(),卢天秀^1,^3,*()

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

收稿日期:2020-09-29 出版日期:2021-10-26 发布日期:2021-10-08
通讯作者: 卢天秀 E-mail:yxf_suse@163.com;80651177@163.com;lubeeltx@163.com
作者简介:杨晓芳, E-mail: yxf_suse@163.com|唐孝, E-mail: 80651177@163.com
基金资助:
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)

The Collectively Sensitivity and Accessible in Non-Autonomous Composite Systems

Xiaofang Yang¹(),Xiao Tang²(),Tianxiu Lu^1,^3,*()

¹ College of Mathematics and Statistics, Sichuan University of Science and Engineering, Sichuan Zigong 643000
² School of Mathematical Science, Sichuan Normal University, Chengdu 610068
³ Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things, Sichuan Zigong 643000

Received:2020-09-29 Online:2021-10-26 Published:2021-10-08
Contact: Tianxiu Lu E-mail:yxf_suse@163.com;80651177@163.com;lubeeltx@163.com
Supported by:
the Science and Technology Plan of Sichuan Province(19YYJC2845);the Key Laboratory of Colleges and Universities Open Fund for Enterprise Information and Internet of Measurement and Control Technology in Sichuan Province(2020WZJ01);the Talent Introduction Program(2020RC24);the Graduate Student Innovation Fund(Y2020077)

摘要/Abstract

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 $(f_{k})_{k=1}^{\infty}$ 是 ${\cal P}$ -混沌的当且仅当 $\forall n\in{\Bbb N}$ ( ${\Bbb N}$ 是自然数集且不含0), 映射序列 $(f_{k})_{k=n}^{\infty}$ 是 ${\cal P}$ -混沌的. 然后, 在 $f_{1, \infty}$ 一致收敛的条件下, 证明了 $f_{1, \infty}$ 具有 ${\cal CP}$ -混沌性当且仅当复合系统 $f_{1, \infty}^{[m]}$ ( $m\in {\Bbb N}$ ) 也具有 ${\cal CP}$ -混沌性. 其中, ${\cal P}$ -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; ${\cal CP}$ -混沌性表示下面四个性质之一: 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.

关键词: 非自治离散系统, 复合映射, 传递性, 敏感性, 可达性

Abstract:

In this paper, collectively sensitivity, collectively infinity sensitivity, collectively Li-Yorke 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 $(f_k)^\infty_{k=1}$ is ${\cal P}$ -chaos if and only if $\forall n\in {\Bbb N}$ ( $N$ is the set of natural numbers and does not contain 0). Then, under the condition that $f_{1, \infty}$ is uniformly convergence, it is proved that $f_{1, \infty}$ is ${\cal CP}$ -chaos if and only if for any $m\in {\Bbb N}$ , $f_{1, \infty}^{[m]}$ is ${\cal CP}$ -chaos. Where ${\cal P}$ -chaos denote one of the five properties: transitivity, sensitivity, infinitely sensitivity, accessibility and exact, ${\cal CP}$ -chaos denote one of the four properties: collectively sensitivity, collectively infinity sensitivity, collectively Li-Yorke sensitivity and collectively accessible.

Key words: Non-autonomous discrete system, Composite mapping, Transitivity, Sensitivity, Accessibility

中图分类号:

O193

杨晓芳,唐孝,卢天秀. 非自治复合系统的集态敏感性和集态可达性[J]. 数学物理学报, 2021, 41(5): 1545-1554.

Xiaofang Yang,Xiao Tang,Tianxiu Lu. The Collectively Sensitivity and Accessible in Non-Autonomous Composite Systems[J]. Acta mathematica scientia,Series A, 2021, 41(5): 1545-1554.

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