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Riccati微分方程特解的向量场分析法
Methods of Vector Field Analysis of Special Solution at Some Riccati Differential Equations
【摘要】 对一般的Riccati微分方程,首先给出了在初值条件下解的存在惟一性定理,然后利用向量场的分析方法对其特解进行逼近,最后得到Riccati方程的特解,并讨论了特解的周期性和稳定性.
【Abstract】 This paper gives the theorem of uniqueness of solution existence at initialization conditions for general Riccati differential equations,tries to reach an approximation for special solution by means of vector field,and finally gets a special solution of Riccati differential equations.It also discusses the periodicity and stability of special solution.
【关键词】 Riccati微分方程;
向量场;
存在惟一性;
周期解;
稳定性.;
【Key words】 Riccati differential equation; vector field; uniqueness of existence; periodic solution; stability;
【Key words】 Riccati differential equation; vector field; uniqueness of existence; periodic solution; stability;
【基金】 河南省教育厅“十五”教育科学规划重点课题项目(2003—JKCHA—163)
- 【文献出处】 西安文理学院学报(自然科学版) ,Journal of Xi’an University of Arts & Science(Natural Science Edition) , 编辑部邮箱 ,2010年04期
- 【分类号】O175.1
- 【被引频次】2
- 【下载频次】68