【摘要】 研究在第一临界情形下的一类特殊的5次多项式微分系统,利用Poincare变换、环域定理、闭轨道星形的特点等方法,得到有关极限环的存在性、唯一性及稳定性的结果;指出第一临界情形下的一类5次系统.至多有一个极限环,如果存在则是稳定的.并给出了存在性条件,进而指出了其所有可能的全局相图,计有64种.更多还原

【Abstract】 Using Poincare transformation and Poincare-Bendixson theorem, sufficient conditions for the existence, uniqueness and stability of the limit cycles for a kind of fifth order differential equation are obtained. It is proved that such a kind of systems has at most one limit cycle and the existence is accompanied by the stability. Furthermore, almost all possible global phase portraits, 64 altogether, are indicated.更多还原