FIVE LIMIT CYCLES TO A CLASS OF SYSTEMS IN R^3  

作　　者：Lianhua Ma, Cuihong Yang , Xinan Zhang (School of Math. and Statistics, Central China Normal University, Wuhan 430079) 

出　　处：《Annals of Differential Equations》2011年第2期190-195,共6页微分方程年刊（英文版）

基　　金：supported by the National Natural Science Foundation of China (No.10701037, No.10871080 and No.10771081)

摘　　要：In this paper, a bridge between near-homogeneous and homogeneous vector fields in R 3 is found. By the relationship between homogeneous vector fields and the induced tangent vector fields of two-dimensional manifold S 2 , we prove the existence of at least 5 isolated closed orbits for a class of n + 1 (n ≥ 2) systems in R 3 , which are located on the five invariant closed cones of the system.In this paper, a bridge between near-homogeneous and homogeneous vector fields in R 3 is found. By the relationship between homogeneous vector fields and the induced tangent vector fields of two-dimensional manifold S 2 , we prove the existence of at least 5 isolated closed orbits for a class of n + 1 (n ≥ 2) systems in R 3 , which are located on the five invariant closed cones of the system.

关 键 词：limit cycle invariant cone vector field 

分 类 号：O183.1[理学—数学]