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[1]李克华,刘粒.脉冲系统中闭集稳定性与集值映射连续性的关系[J].厦门理工学院学报,2021,29(1):91-96.[doi:1019697/jcnki16734432202101014]
 LI Kehua,LIU Li.Relationships Between Stability of Closed Sets and Continuity ofSetvalued Maps in Impulsive Dynamical Systems[J].Journal of JOURNAL OF XIAMEN,2021,29(1):91-96.[doi:1019697/jcnki16734432202101014]
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脉冲系统中闭集稳定性与集值映射连续性的关系(PDF/HTML)
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《厦门理工学院学报》[ISSN:1673-4432/CN:35-1289/Z]

卷:
29
期数:
2021年第1期
页码:
91-96
栏目:
应用数理科学
出版日期:
2021-02-28

文章信息/Info

Title:
Relationships Between Stability of Closed Sets and Continuity of Setvalued Maps in Impulsive Dynamical Systems
文章编号:
16734432(2021)01009106
作者:
李克华刘粒
厦门理工学院应用数学学院,福建 厦门 361024
Author(s):
LI KehuaLIU Li
School of Applied Mathematics,Xiamen University of Technology,Xiamen 361024,China
关键词:
脉冲动力系统正延伸集正延伸极限集稳定性 极限集映射 半连续性
Keywords:
impulsive dynamical systemspositive prolongationspositive prolongational limit setsstabilitysetvalued mapssemicontinuity
分类号:
O192
DOI:
1019697/jcnki16734432202101014
文献标志码:
A
摘要:
为进一步探讨脉冲动力系统中闭集的局部稳定性和集值映射的连续性的关系,在脉冲动力系统中引入闭集在某一点处稳定的定义及其等价条件,参照一般连续动力系统中的情形,以度量空间中的HAUSDORFF度量为工具,讨论脉冲动力系统中两类特殊的闭集,即正延伸集和正延伸极限集的稳定性与相应的集值映射的连续性之间的关系。研究表明:集值映射D+(或K+)在x点上半连续当且仅当集合D+(x)(或K+(x))在x点稳定,映射L+在x点上半连续当且仅当闭集L+(x)在x点最终稳定,映射J+在x点上半连续,蕴含着闭集J+(x)在x点最终稳定,反之,若J+(x)在x点一致最终稳定,那么映射J+在x点上半连续。
Abstract:
In this paper,we deal with the relationship between the local stability of closed sets and the continuity of setvalued maps in impulsive dynamical systems.We introduce the definition of stability for closed sets at a point and its equivalent conditions,and investigate by HAUSDORFF metric the relationships between the stability of two special closed sets—positive prolongations and positive prolongational limit sets—and the continuity of corresponding setvalued maps,as in the case of continuous dynamical systems.It shows that the map D+(orK+) is upper semicontinuous at x if and only if closed set D+(x)(orK+(x)) is stable at x,the map L+is upper semicontinuous at x if and only if closed set L+(x) is eventually stable at x,the map J+is upper semicontinuous at x implies L+(x) is eventually stable at xand conversely,if L+(x) has uniform eventual stability at x,then J+ is upper semicontinuous at x.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:20200901修回日期:20201030 〗基金项目:福建省客车及特种车协同创新项目(2016BJC002);厦门理工学院高层次人才科研项目(YKJ15029R) 通信作者:李克华,男,讲师,博士,研究方向为拓扑动力系统,Email:khli@xmuteducn。
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