A CUBIC SYSTEM WITH 8 SMALL-AMPLITUDE LIMIT-CYCLES

被引：14

作者：

NING, SC

MA, SL

KWEK, KH

ZHENG, ZM

机构：

[1] BEIJING UNIV AERONAUT & ASTRON,DEPT COMP SCI,BEIJING 100083,PEOPLES R CHINA

[2] NATL UNIV SINGAPORE,DEPT MATH,SINGAPORE 0511,SINGAPORE

[3] BEIJING UNIV,DEPT MATH,BEIJING 100871,PEOPLES R CHINA

来源：

APPLIED MATHEMATICS LETTERS | 1994年 / 7卷 / 04期

基金：

美国国家科学基金会;

关键词：

LIMIT CYCLES; FINE FOCUS; PERTURBATION; SYMBOLIC COMPUTATION; ORDERING;

D O I：

10.1016/0893-9659(94)90005-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In E.M. James and N.G. Lloyd's paper A Cubic System with Eight Small-Amplitude Limit Cycles [1], a set of conditions is given that ensures the origin to be a fine focus of order eight and eight limit cycles to bifurcate from the origin by perturbing parameters. We find that one of the conditions, a9 = sigma*a7, where 666/97 < sigma* < 103/15, can be weakened as a9 = sigma.a7 or a9 = sigma1a7, where 283/125 < sigma1 < 284/125. In [1], deriving above conditions is reduced to finding the real solutions of a system of some algebraic equations and inequalities. When verifying these conditions by solving this system in a different ordering, we find another real solution to the system, which is leading to above improvement of the conditions.

引用

页码：23 / 27

页数：5