Number and Location of Limit Cycles in a Class of Perturbed Polynomial Systems  

作　　者：Chen-xiYang Rui-qiWang 

机构地区：[1]DepartmentofMathematics,YuxiNormalCollege,Yuxi653100,China [2]AcademyofMathematicsandSystemsScience,AcademiaSinica,Beijing,100080,China

出　　处：《Acta Mathematicae Applicatae Sinica》2004年第1期155-166,共12页应用数学学报（英文版）

基　　金：Supported by Natural Science Foundation of China (10261008);"Creative Project"(KZCZ2-SW-118) in Chinese Academy of Sciences

摘　　要：In this paper,we investigate the number,location and stability of limit cycles in a class of perturbedpolynomial systems with (2n+1) or (2n+2)-degree by constructing detection function and using qualitativeanalysis.We show that there are at most n limit cycles in the perturbed polynomial system,which is similar tothe result of Perko in [8] by using Melnikov method.For n=2,we establish the general conditions dependingon polynomial's coefficients for the bifurcation,location and stability of limit cycles.The bifurcation parametervalue of limit cycles in [5] is also improved by us.When n=3 the sufficient and necessary conditions for theappearance of 3 limit cycles are given.Two numerical examples for the location and stability of limit cycles areused to demonstrate our theoretical results.In this paper,we investigate the number,location and stability of limit cycles in a class of perturbedpolynomial systems with (2n+1) or (2n+2)-degree by constructing detection function and using qualitativeanalysis.We show that there are at most n limit cycles in the perturbed polynomial system,which is similar tothe result of Perko in [8] by using Melnikov method.For n=2,we establish the general conditions dependingon polynomial's coefficients for the bifurcation,location and stability of limit cycles.The bifurcation parametervalue of limit cycles in [5] is also improved by us.When n=3 the sufficient and necessary conditions for theappearance of 3 limit cycles are given.Two numerical examples for the location and stability of limit cycles areused to demonstrate our theoretical results.

关 键 词：polynomial system limit cycles stability BIFURCATION 

分 类 号：O15[理学—数学] O174.4[理学—基础数学]