摘要
对一类非线性振动方程进行定性分析与探究,并推广了此类方程。采用行列式-迹法则、小参数扰动、首次积分和Bendixson-Dulac判别法。证明了方程对任何参数都不存在闭轨线和奇异闭轨线,分析了方程在特殊情形下奇点个数、类型。丰富了已知结果,使其适用范围更广。
To do qualitative analysis of and exploration for a special type of vibration equation, at last me promotion and extension of the equation were done. The determinant of trace rule, small parameter perturbation, the first integral and Bendixson-Dulae diseriminant are applied into the analysis on the vibration equation for qualitative analysis. Under different parameters, the number and type of singularities was proved. In the sequel, to prove that the equation for any parameters doesn＇t exist closed trajectories and the singular closed trajectories. The obtained results improve and expand the related known works.
出处
《西北大学学报（自然科学版）》
CAS
CSCD
北大核心
2016年第4期469-474,共6页
Journal of Northwest University（Natural Science Edition）
基金
西北大学研究生自主创新基金资助项目(YZZ14083)
陕西省教育厅自然科学专项基金资助项目(CU063120603000)
关键词
振动方程
定性分析
闭轨线
极限环
Dulac判别法
vibration equation
qualitative analysis
closed trajectories
limit cycle
Dulac discriminant method
