非线性与线性微分系统的等价关系研究（英文）  

On the relationship between nonlinear and linear differential systems

作　　者：周正新[1] 毛妨妨 郭影影[1] 王斐[1] 陈雅媛 

机构地区：[1]扬州大学数学科学学院,扬州225002

出　　处：《上海师范大学学报（自然科学版）》2015年第3期322-329,共8页Journal of Shanghai Normal University(Natural Sciences)

基　　金：supported by the NSF of China(61374010);the NSF of Jiangsu Province(BK2012682);2014-SSF of Yangzhou University

摘　　要：建立了一类时变非线性微分系统与线性微分系统之间的等价关系,给出了一类二次微分系统具有有理分式形式的反射函数的充分条件。并应用所得结论研究了二次微分系统及时变Kolmogrov系统的周期解及其定性性态.In this article, we establish the relationship between the quadratic time-varying differential systems and the linear systems, giving the sufficient conditions for the quadratic systems to have the reflecting function in the form of fractional function. We use the obtained results to discuss the qualitative behavior of the solutions of the quadratic differential systems and the time-varying Kolmogrov equations.

关 键 词：反射函数 周期解 时变系统 

分 类 号：O175.12[理学—数学]