一类非线性二维自治系统的两个重合着的极限环  

Two Duplicate Limits Cycles of a Kind of Nonlinear Two-Dimension Autonomous System

作　　者：王晓静[1] 崔景安[1] 叶萌[1] 许传青[1] 

机构地区：[1]北京建筑大学理学院数学系,北京100044

出　　处：《大学数学》2015年第4期64-69,共6页College Mathematics

基　　金：国家自然科学基金(11371048);北京建筑大学双语课程建设(常微分方程);北京建筑大学稳定性理论优质课程(K2015004)

摘　　要：利用《微分积分法软件》和微分方程定性理论研究了一类二维非线性自治系统的动力学性质.探讨了五个平衡点的存在性、稳定性和极限集等一些几何性质,并通过描绘系统的图像解,得到两个重合的横置的葫芦形极限环.在解题的过程中首次发现了一个反常的现象:此系统所描述的周期性运动其周期的大小随自变量的微分的减小而增大.The dynamic properties of a class of nonlinear two-dimension autonomous system are investigated based on the differential and integral method and the qualitative theory of differential equations. The existence and stability of five equilibria, limit sets and some other geometric properties are obtained. From the image solution, we get two duplicate limit cycles with transverse gourd shaped. An abnormal phenomenon was first discovered in the process of studying~ the period of the periodic motion increases as the derivative of the independent variable decreases.

关 键 词：平衡点 稳定性 周期解 极限环 

分 类 号：O175[理学—数学]