一类高次多项式系统极限环的研究及其应用

Study on a Class of Higher Polynomial System and Its Application

应用平面自治系统的极限环理论和分支理论 ,研究了一类具有普遍意义的高次多项式系统 .讨论了该系统极限环的存在性和惟一性 ,分析了系统的分支 ,同时解决了系统极限环的个数和分布问题 .

A class of higher polynomial system with great significance is researched with the theory of limit cycles and bifurcation of the plane autonomous system.The existence and uniqueness of its limit cycles and its bifurcations are analyzed,at the same time.The problems of the number and location of the limit cycles are solved.