广东工业大学学报 ›› 2020, Vol. 37 ›› Issue (06): 56-62.doi: 10.12052/gdutxb.190160

• • 上一篇    下一篇

一类脉冲随机微分方程解的稳定性

黄慧敏, 郭承军   

  1. 广东工业大学 应用数学学院，广东 广州 510520
  • 收稿日期:2019-12-19 出版日期:2020-11-02 发布日期:2020-11-02
  • 通信作者: 郭承军(1977-)，男，教授，主要研究方向为泛函微分方程，E-mail：guochj817@163.com E-mail:guochj817@163.com
  • 作者简介:黄慧敏(1995-)，女，硕士研究生，主要研究方向为泛函微分方程
  • 基金资助:
    广东省自然科学基金资助项目（2018A030313871）

Stability of Solutions for a Class of Impulsive Stochastic Differential Equations

Huang Hui-min, Guo Cheng-jun   

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2019-12-19 Online:2020-11-02 Published:2020-11-02

HTML

PDF (PC)

2694

摘要： 通过运用不动点理论方法和Lyapunov稳定性定理，研究了一类脉冲随机微分方程解的稳定性，得到了该方程均方指数稳定的充分条件。

关键词: 不动点理论, Lyapunov泛函, 脉冲, 稳定性

Abstract: The stability of solutions of a class of impulsive stochastic differential equations was studied by using the fixed point theory and Lyapunov stability theorem and sufficient conditions for the exponential stability in the mean square of the equation are obtained.

Key words: fixed point theory, Lyapunov functional, impulsive, stability

中图分类号: 

  • O175
[1] LIU K. Stability of infinite dimensional stochastic differential equations with applications[M]. London: Chapman & Hall/CRC, 2005.
[2] MAO X R. Exponential stability in mean square of neutral stochastic differential functional equations [J]. Systems and Control Letters, 1995, 26(4): 245-251.
[3] GUO C J, O’REGAN D, DENG F Q. Fixed points and exponential stability for a stochastic neutral cellular network [J]. Applied Mathematics Letters, 2013, 26(8): 849-853.
[4] LI D S, FAN X M. Exponential stability of impulsive stochastic partial differential equations with delays [J]. Statistics and Probability Letters, 2017, 126: 185-192.
[5] HU W, ZHU Q X. Moment exponential stability of stochastic nonlinear delay systems with impulse effects at random times [J]. International Journal of Robust and Nonlinear Control, 2009, 29: 3809-3820.
[6] FU X Z, ZHU Q X, GUO Y X. Stabilization of stochastic functional differential systems with delayed impulses [J]. Applied Mathematics and Computation, 2019, 346: 776-789.
[7] YU G S, YANG W Q, XU L. Pth moment and almost sure exponential stability of impulsive neutral stochastic functional differential equations with markovian switching [J]. International Journal of Systems Science, 2018, 49(6): 1164-1177.
[8] LUO J W. Fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays [J]. Journal of Mathematical Analysis and Applications, 2008, 342(2): 753-760.
[9] 徐林, 宋常修. 一类三阶时滞微分方程的稳定性和有界性[J]. 广东工业大学学报, 2015, 32(1): 128-132.
XU L, SONG C X. Stability and boundedness of a class of third-order delay differential equations [J]. Journal of Guangdong University of Technology, 2015, 32(1): 128-132.
[10] CHENGUP, DENG F Q. Global exponential stability of impulsive stochastic functional Differential systems [J]. Statistics and Probability Letters, 2010, 80(23-24): 1854-1862.
[11] CHENGUP, DENGUF Q, YAOUF Q. Almost sure exponential stability and stochastic stabilization of stochastic differential systems with impulsive effects [J]. Nonlinear Analysis Hybrid Systems, 2018, 30: 106-117.
[12] CUI J, YAN L T. Asymptotic behavior for neutral stochastic partial differential equations with infinite delays [J]. Electronic Communications in Probability, 2013, 18(45): 1-12.
[13] CHEN G L, GAANS O V, LUNEL S V. Existence and exponential stability of a class of impul- sive neutral stochastic partial differential equations with delays and Poisson jumps [J]. Statistics and Probability Letters, 2018, 141: 7-18.
[14] MAO X R. Stochastic differential equations and applications[M]. Chichestic: Horwood Publishing Limited, 2007.
[15] XU Y, HE Z M. Exponential stability of neutral stochastic delay differential equations with Markovian switching [J]. Applied Mathematics Letters, 2016, 52: 64-73.
[1] 陈靖宇, 吕毅. 基于脉冲神经网络的冷链制冷机结霜检测方法[J]. 广东工业大学学报, 2023, 40(01): 29-38.
[2] 谷志华, 彭世国, 黄昱嘉, 冯万典, 曾梓贤. 基于事件触发脉冲控制的具有ROUs和RONs的非线性多智能体系统的领导跟随一致性研究[J]. 广东工业大学学报, 2023, 40(01): 50-55.
[3] 邹翀, 唐雄民, 陈伟正, 江天鸿, 方文睿. 脉冲电流源作用下大气压介质阻挡放电的特性分析[J]. 广东工业大学学报, 2022, 39(04): 36-45.
[4] 刘雪, 刘忠明, 席跃宾, 王守娟, 孔凡功. 木质素基超疏水涂层的制备及其应用性能研究[J]. 广东工业大学学报, 2022, 39(01): 34-40,134.
[5] 唐浩怡, 彭红云. 三维趋化系统全局弱解的存在性和渐近稳定性[J]. 广东工业大学学报, 2022, 39(01): 93-98.
[6] 郑子钊, 彭世国, 付志文, 徐云剑. 脉冲控制下一类多权重复杂网络的鲁棒H∞同步[J]. 广东工业大学学报, 2021, 38(03): 55-61.
[7] 周民华, 张文进, 潘春阳. 镓离子掺杂的CsPbBr3量子点的制备及其性能研究[J]. 广东工业大学学报, 2021, 38(02): 83-87.
[8] 梁仕华, 陈俊涛, 林焕生, 冯德銮, 龚星, 罗庆姿. 水泥固化淤泥废弃土作为填土材料的试验研究[J]. 广东工业大学学报, 2020, 37(02): 102-106.
[9] 刘陈霖, 郑三强, 韩晓卓. 具有Allee效应捕食-竞争系统的时空动态分析[J]. 广东工业大学学报, 2019, 36(06): 38-44.
[10] 张会琴, 汪志波. 带周期边界的时间分数阶扩散方程的差分格式[J]. 广东工业大学学报, 2019, 36(03): 74-79.
[11] 汪翔, 刘立凡, 王志红, 漆文光. 优质地表水源突发污染后长距离输水水质稳定性研究[J]. 广东工业大学学报, 2019, 36(03): 99-102,110.
[12] 刘铭炜, 禹智涛, 贺绍华. 基于统一理论的钢管混凝土拱桥稳定性分析[J]. 广东工业大学学报, 2018, 35(06): 63-68.
[13] 张振华, 彭世国. 二阶多智能体系统拓扑切换下的领导跟随一致性[J]. 广东工业大学学报, 2018, 35(02): 75-80.
[14] 庄小兰, 王琦. 一阶时滞微分方程欧拉法的动力性[J]. 广东工业大学学报, 2018, 35(01): 46-49.
[15] 赵腾起, 朱燕娟, 李文华, 简修文, 罗洁, 张伟, 张春华. 掺杂氢氧化镍晶相及其结构稳定性与碳酸钠用量的关系研究[J]. 广东工业大学学报, 2016, 33(04): 56-61.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2017 《广东工业大学学报》编辑部
地址：广州市东风东路729号广东工业大学 邮编：510090
电话：020-37626653,020-37626139,020-37626396
邮箱：xbzrb@gdut.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发