一类由α-稳定过程驱动的随机时滞微分方程的LaSalle不变原理

doi:10.3969/j.issn.1000-5641.2023.04.002

华东师范大学学报（自然科学版） ›› 2023, Vol. 2023 ›› Issue (4): 11-23.doi: 10.3969/j.issn.1000-5641.2023.04.002

一类由α-稳定过程驱动的随机时滞微分方程的LaSalle不变原理

张振中(), 陈旭, 童金英

东华大学理学院, 上海　201620

收稿日期:2021-09-24 出版日期:2023-07-25 发布日期:2023-07-25
作者简介:张振中, 男, 教授, 研究方向为受控的混杂跳扩散系统及应用. E-mail: zzzhang@dhu.edu.cn
基金资助:
国家自然科学基金 (12171081); 上海市自然科学基金 (22WZ2505700, 23ZR1402600); 东华大学虚拟仿真实验教学项目; 东华大学一流本科课程(DHYLA-2022-23); 东华大学偏微分方程示范教研室(SFJYS2021-05)

LaSalle’s invariance principle for delay differential equations driven by α-stable processes

Zhenzhong ZHANG(), Xu CHEN, Jinying TONG

College of Science, Donghua University, Shanghai　201620, China

Received:2021-09-24 Online:2023-07-25 Published:2023-07-25

摘要/Abstract

摘要：

LaSalle 不变原理是研究随机系统稳定性的重要工具. 考虑到时滞与样本轨道跳跃对系统稳定性的影响, 本文通过特殊半鞅的收敛性, 建立了一类由 $\alpha$ -稳定过程驱动的随机时滞微分方程的 LaSalle 不变原理. 利用 LaSalle 不变原理给出了一类延迟方程解渐进稳定的充分条件.

关键词: LaSalle 不变原理, 特殊半鞅, 依概率渐近稳定性, 依概率稳定性

Abstract:

LaSalle’s invariance principle is an important tool for studying the stability of stochastic systems. Considering the influence of time delay and pure-jump path on the stability of the system and using the convergence theorem for special semi-martingale, the LaSalle’s invariance principle for a class of stochastic delay differential equations driven by $\alpha$ -stable processes is established in this study. The sufficient conditions for the asymptotic stability of a class of delay equations are given by LaSalle’s invariance principle.

Key words: LaSalle’s invariance principle, special semi-martingale, asymptotic stability in probability, stability in probability

中图分类号:

O211.63

张振中, 陈旭, 童金英. 一类由α-稳定过程驱动的随机时滞微分方程的LaSalle不变原理[J]. 华东师范大学学报（自然科学版）, 2023, 2023(4): 11-23.

Zhenzhong ZHANG, Xu CHEN, Jinying TONG. LaSalle’s invariance principle for delay differential equations driven by α-stable processes[J]. Journal of East China Normal University(Natural Science), 2023, 2023(4): 11-23.

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一类由α-稳定过程驱动的随机时滞微分方程的LaSalle不变原理

LaSalle’s invariance principle for delay differential equations driven by α-stable processes

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