Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four

被引：2

作者：

Saez, Eduardo

Stange, Eduardo

Szanto, Ivan

机构：

[1] Univ Tecn Federico Santa Maria, Dept Matemat, Valparaiso, Chile

[2] Univ Valparaiso, Inst Math & Fis, Valparaiso 5030, Chile

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2007年 / 57卷 / 01期

关键词：

stability; limit cycle; center; bifurcation;

D O I：

10.1007/s10587-007-0047-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A class of degree four differential systems that have an invariant conic x(2) + Cy-2 = 1, C epsilon R, is examined. We show the coexistence of small amplitude limit cycles, large amplitude limit cycles, and invariant algebraic curves under perturbations of the coefficients of the systems.

引用

页码：105 / 114

页数：10

共 36 条

[1]

Bautin N., 1952, MAT SBORNIK, V72, P181

[2]

BENDIXSON I, 1900, ACTA MATH, V24, P1

[3] Coexistence of limit cycles and invariant algebraic curves for a Kukles system [J].

Chavarriga, J ;

Sáez, E ;

Szántó, I ;

Grau, M .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 59 (05) :673-693

[4]

Cherkas L.A., 1972, DIFFER URAVNENIYA, V8, P924

[5] QUADRATIC SYSTEMS HAVING A PARABOLA AS AN INTEGRAL CURVE [J].

CHRISTOPHER, C .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1989, 112 :113-134

[6]

Coppel WA., 1989, Dynamics Reported: A Series in Dynamical Systems and Their Applications, P61, DOI [10.1007/978-3-322-96657-5_3, DOI 10.1007/978-3-322-96657-5_3]

[7]

COZMA D, 1999, AN STIINT U AL CUZ S, V44, P517

[8]

Cozma D., 2001, Qual. Theory Dyn. Syst, V2, P129, DOI [10.1007/BF02969386, DOI 10.1007/BF02969386]

[9]

DONGMING W, 1990, J DIFFER EQUATIONS, V87, P305

[10]

DULAC H, 1923, S M F B, V51, P45

← 1 2 3 4 →