Riccati方程的广义反射函数与周期解  

Generalized reflection function and periodic solution of Riccati equation

作　　者：孙长军[1] 

机构地区：[1]连云港职业技术学院数学教研室,江苏连云港222000

出　　处：《辽宁工程技术大学学报（自然科学版）》2011年第4期596-598,共3页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金资助项目(60774073);江苏省教委自然科学研究基金资助项目(08KJB110013)

摘　　要：为了解决Riccati方程的周期解与稳定性,提出了通过Riccati方程的广义反射函数来寻找其Poincaré映射的方法。结果表明:从微分系统的广义反射函数角度出发,得到了Riccati方程具有线性广义反射函数的条件,从而推出了Riccati方程的线性广义反射函数,得到了Riccati方程的Poincaré映射,以及Riccati方程有周期解的条件与稳定性。由于通过广义反射函数寻找Poincaré映射比较简单可行,所以,Riccati方程的周期解与稳定性的研究成果对其它微分系统的研究也具有指导作用。In order to solve the problem associated with Riccati equation periodic solution and stability,this paper proposes a method to find its Poincaré mapping through Riccati equation＇s generalized reflection function.The result indicates that based on differential system＇s generalized reflection function,the condition that enables Riccati equation to have the linear generalized reflection function is obtained,the linear generalized reflection function of Riccati equation is derived,Poincaré mapping of Riccati equation and the condition that enables Riccati equation to have periodic solution and stability are obtained.Because it is simple and feasible to find Poincaré mapping through the generalized reflection function,therefore,the study results on the Riccati equation＇s periodic solution and stability are also of significance to the study of other differential system.

关 键 词：广义反射函数 RICCATI方程 POINCARÉ映射 周期解 稳定性 微分系统 线性广义反射函数 微分系统的广义反射函数 

分 类 号：O187[理学—数学]