摘要
目的为讨论一类平面微分系统极限环的存在惟一性及不存在性。方法运用G．Sansone 定理和旋转向量场理论对此类平面微分系统极限环的存在惟一性进行了讨论。结果得到了此类系统极限环的存在惟一性及不存在性的完整分析。结论与传统方法相比,运用G．Sansone定理和旋转向量场理论对此类平面微分系统极限环的存在惟一性及其稳定性进行分析,得到了完整的结果。
Aim In order to discuss the existence and uniqueness of limit cycles for a class of planar differential systems. Methods G. Sansone theorem and rotated vector fields are applied to discuss the existence and uniqueness of limit cycles for the planar differential systems. Results The existence, uniqueness and nonexistence of limit cycles are analyzed and discussed. Conclusion Compared with traditional method, the complete results on the existence and uniqueness of limit cycles for the planar differential systems are obtained by means of G. Sansone theorem and rotated vector fields.
出处
《西北大学学报（自然科学版）》
CAS
CSCD
北大核心
2006年第2期183-185,共3页
Journal of Northwest University（Natural Science Edition）
基金
国家科技攻关计划项目(2004BA719A01)空军工程大学理学院科研基金资助项目
关键词
平面微分系统
极限环
存在惟一性
planar differential systems
limit cycles
existence and uniqueness
