一类非线性奇异摄动自治微分系统的渐近解

冯依虎; 陈怀军; 莫嘉琪

doi:10.21656/1000-0887.380110

一类非线性奇异摄动自治微分系统的渐近解

doi: 10.21656/1000-0887.380110

¹亳州学院电子与信息工程系, 安徽亳州 236800;²安徽师范大学数学计算机科学学院, 安徽芜湖 241003

基金项目: 国家自然科学基金(11202106);安徽省教育厅自然科学重点基金(KJ2015A347;KJ2017A702);安徽省高校优秀青年人才支持计划重点项目(gxyqZD2016520)

详细信息

作者简介:
冯依虎(1982—），男，副教授，硕士（E-mail: fengyihubzsz@163.com）;莫嘉琪(1937—),男,教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

中图分类号: O175.19
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出版历程
- 收稿日期: 2017-04-25
- 修回日期: 2017-06-07
- 刊出日期: 2018-03-15

Asymptotic Solution to a Class of Nonlinear Singular Perturbation Autonomous Differential Systems

¹Department of Electronics and Information Engineering, Bozhou College, Bozhou, Anhui 236800, P.R.China;²School of Mathematics & Computer Science, Anhui Normal University, Wuhu, Anhui 241003, P.R.China

Funds: The National Natural Science Foundation of China(11202106)

摘要

摘要: 研究了一类广义Lienard奇异摄动系统.首先, 求出了系统的退化解；其次, 利用奇异摄动方法得到了系统的外部解，并用伸长变量方法, 求得了系统的初始层校正项；最后, 得到了系统解的任意次渐近解析展开式，并证明了解的一致有效性.该文所用的方法和理论, 具有广泛的实际应用价值.
- 伸长变量 /
- 奇异摄动 /
- 自治系统
Abstract: A class of generalized Lienard singular perturbation systems were considered. Firstly, the reduced solution to the system was obtained. Next, the outer solution was constructed by means of the singular perturbation method. Then, a stretch variable was introduced and the initial layer corrective term was found. Finally, the arbitrary-order asymptotic analytic expansion of the system solution was given and the uniform validity of the solution was proved. The proposed method with the basic theory has wide application values.
- stretch variable /
- singular perturbation /
- autonomous system

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参考文献(27)

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文章访问数: 1354
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PDF下载量: 485
被引次数: 0

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一类非线性奇异摄动自治微分系统的渐近解

doi: 10.21656/1000-0887.380110

作者简介:
冯依虎(1982—），男，副教授，硕士（E-mail: fengyihubzsz@163.com）;莫嘉琪(1937—),男,教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

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Asymptotic Solution to a Class of Nonlinear Singular Perturbation Autonomous Differential Systems

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留言板

一类非线性奇异摄动自治微分系统的渐近解

doi: 10.21656/1000-0887.380110

作者简介: 冯依虎(1982—），男，副教授，硕士（E-mail: fengyihubzsz@163.com）;莫嘉琪(1937—),男,教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

计量

出版历程

Asymptotic Solution to a Class of Nonlinear Singular Perturbation Autonomous Differential Systems

计量

出版历程

目录

作者简介:
冯依虎(1982—），男，副教授，硕士（E-mail: fengyihubzsz@163.com）;莫嘉琪(1937—),男,教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).