Cubic system with eight small-amplitude limit cycles

被引：0

作者：

James, E.M. ^{[1
]}

Lloyd, N.G. ^{[1
]}

机构：

[1] Univ Coll of Wales, Aberystwyth, United Kingdom

来源：

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) | 1991年 / 47卷 / 02期

基金：

美国国家科学基金会;

关键词：

Mathematical Techniques - Differential Equations;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In much recent research on Hilbert's sixteenth problem, limit cycles which arise by bifurcation have been investigated. It has long been known that in quadratic systems at most three limit cycles can bifurcate from a critical point, and that the maximum number in symmetric cubic systems is five. Examples exist in the literature of cubic systems with six small-amplitude limit cycles. In this paper, a class of cubic systems with eight such limit cycles is described.

引用

页码：163 / 171

共 50 条

[21] Small-amplitude limit cycle bifurcations for Lienard systems with quadratic or cubic damping or restoring forces
Christopher, C
Lynch, S
NONLINEARITY, 1999, 12 (04) : 1099 - 1112
[22] Seven large-amplitude limit cycles in a cubic polynomial system
Liu, YR
Huang, WT
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2006, 16 (02): : 473 - 485
[23] Deriving some new conditions on the existence of eight limit cycles for a cubic system
Ma, SL
Ning, SC
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1997, 33 (07) : 59 - 84
[24] BIFURCATIONS OF LIMIT CYCLES FOR A PERTURBED CUBIC SYSTEM WITH DOUBLE FIGURE EIGHT LOOP
Zhang, Tonghua
Zang, Hong
Tade, Mose O.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2013, 23 (04):
[25] SMALL-AMPLITUDE LIMIT OF THE NUCLEAR BORN-OPPENHEIMER METHOD
ZETTILI, N
PHYSICAL REVIEW C, 1995, 51 (04) : 1777 - 1783
[26] Limit Cycles of A Cubic Kolmogorov System
Li, Feng
PROCEEDINGS OF THE 7TH CONFERENCE ON BIOLOGICAL DYNAMIC SYSTEM AND STABILITY OF DIFFERENTIAL EQUATION, VOLS I AND II, 2010, : 619 - 622
[27] Limit cycles of a cubic Kolmogorov system
Lloyd, NG
Pearson, JM
Saez, E
Szanto, I
APPLIED MATHEMATICS LETTERS, 1996, 9 (01) : 15 - 18
[28] Bifurcations of limit cycles in a cubic system
Zhang, TH
Zang, H
Han, MA
CHAOS SOLITONS & FRACTALS, 2004, 20 (03) : 629 - 638
[29] A cubic system with thirteen limit cycles
Li, Chengzhi
Liu, Changjian
Yang, Jiazhong
JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (09) : 3609 - 3619
[30] Small-amplitude limit cycles of some Lienard-type systems (vol 71, pg 6373, 2009)
Jiang, Jiao
Han, Maoan
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (06) : 3235 - 3235

← 1 2 3 4 5 →