一类具时滞的二阶非线性系统的定性分析

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Qualitative Analysis for a Class of Second Order Nonlinear System with Delay

Department of Basic Science, Suqian Vocational and Technological College, Suqian, Jiangsu 223800

摘要: 考虑具时滞的二阶非线性系统x"(t)+f(x(t),x'(t))+g(x(t),x'(t))ψ(x(t-τ))=p(t).借助李雅普诺夫函数方法,得到了其零解稳定性,解的有界性,周期解的存在性和平稳振荡的存在唯一性.
- 二阶非线性系统 /
- 时滞 /
- 李雅普诺夫函数
Abstract: The second order nonlinear system with delay x"(t)+f(x(t),x'(t))+g(x(t),x'(t))ψ(x(t-τ))=p(t) being considered. Four theorems on the stability of zero solution, the boundedness of the solutions, the existence of the periodic solutions, the existence and uniqueness of the stationary oscilation are obtained by means of the Liapunov's second method. The conclusion in the literatures are generalized.
- second order nonlinear differential equation /
- delay /
- Liapunov functional

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