非线性中立型变延迟微分方程的长时间稳定性

数学物理学报 ›› 2018, Vol. 38 ›› Issue (1): 96-109.

非线性中立型变延迟微分方程的长时间稳定性

王晚生, 钟鹏, 赵新阳

长沙理工大学大学数学与统计学院长沙 410114

收稿日期:2016-03-27 修回日期:2017-04-15 出版日期:2018-02-26 发布日期:2018-02-26
作者简介:王晚生,w.s.wang@163.com;钟鹏,1160885528@qq.com;赵新阳,1160885528@qq.com
基金资助:
国家自然科学基金（11371074，11771060），湖南省自然科学基金杰出青年项目（13JJ1020），湖南省教育厅研究基金（13A108）和湖南省研究生创新项目（CX2016B418）

Long-Time Stability of Nonlinear Neutral Differential Equations with Variable Delay

Wang Wansheng, Zhong Peng, Zhao Xinyang

School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114

Received:2016-03-27 Revised:2017-04-15 Online:2018-02-26 Published:2018-02-26
Supported by:
Supported by the NSFC (11371074, 11771060), the Natural Science Foundation for Distinguished Young scholars in Hunan Province (13JJ1020), the Research Foundation of Education Bureau of Hunan Province (13A108) and the Hunan Graduate Innovation Project (CX2016B418)

摘要/Abstract

摘要： 该文主要分析非线性中立型变延迟微分方程（NDDEs）的长时间行为，获得了非线性变延迟系统解的一致最终有界性的主要结果.基于此主要结果，得到了非线性中立型延迟微分方程的两个典型特例，常延迟微分方程和比例延迟微分方程，解一致最终有界的充分条件.文章最后给出了一些具体实例以说明这些结果的应用.

关键词: 中立型延迟微分方程, 变延迟, 长时间稳定性, 渐近行为, 一致最终有界性, 耗散性

Abstract: The long-time behaviour of nonlinear neutral delay differential equations (NDDEs) with variable delay is analysed. A main result guaranteeing uniform ultimate boundedness for a variable delay nonlinear system has been established. The sufficient conditions for the uniform ultimate boundedness for two typical examples of NDDEs, the constant delay differential equations and the proportional delay differential equations, are derived from the main result. Some examples are given to illustrate the applications of these results.

Key words: Neutral delay differential equations, Variable delay, Long-time stability, Asymptotic behaviour, Uniform ultimate boundedness, Dissipativity

中图分类号:

O177

王晚生, 钟鹏, 赵新阳. 非线性中立型变延迟微分方程的长时间稳定性[J]. 数学物理学报, 2018, 38(1): 96-109.

Wang Wansheng, Zhong Peng, Zhao Xinyang. Long-Time Stability of Nonlinear Neutral Differential Equations with Variable Delay[J]. Acta mathematica scientia,Series A, 2018, 38(1): 96-109.

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