ON BIFURCATION OF LIMIT-CYCLES FROM CENTERS

被引：0
作者：
CHICONE, C
机构：
来源：
LECTURE NOTES IN MATHEMATICS | 1990年 / 1455卷
关键词：
LIMIT CYCLES; CENTER BIFURCATIONS; MULTIPLE HOPF BIFURCATION;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For a one parameter family of plane vector fields X(., epsilon) depending analytically on a small real parameter epsilon, we determine the number and position of the local families of limit cycles which emerge from the periodic trajectories surrounding a center. Aside from the intrinsic interest in the example we choose, it serves to illustrate some techniques which are developed for treating similar bifurcation problems when the first order methods are inconclusive. Actually, we are able to treat the bifurcations of all orders.
引用
收藏
页码：20 / 43
页数：24
相关论文
共 50 条
[31]   Nondegenerate centers and limit cycles of cubic Kolmogorov systems [J].
Antonio Algaba ;
Cristóbal García ;
Jaume Giné .
Nonlinear Dynamics, 2018, 91 :487-496
[32]   Nondegenerate centers and limit cycles of cubic Kolmogorov systems [J].
Algaba, Antonio ;
Garcia, Cristobal ;
Gine, Jaume .
NONLINEAR DYNAMICS, 2018, 91 (01) :487-496
[33]   Algebraic approximations to bifurcation curves of limit cycles for the Lienard equation [J].
Giacomini, H ;
Neukirch, S .
PHYSICS LETTERS A, 1998, 244 (1-3) :53-58
[34]   Bifurcation of limit cycles from a 4-dimensional center in Rm in resonance 1: N [J].
Barreira, Luis ;
Llibre, Jaume ;
Valls, Claudia .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 389 (02) :754-768
[35]   Simultaneous zip bifurcation and limit cycles in three dimensional competition models [J].
Sáez, E ;
Stange, E ;
Szánto, I .
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2006, 5 (01) :1-11
[36]   Perturbed Euler top and bifurcation of limit cycles on invariant Casimir surfaces [J].
Garcia, Isaac A. ;
Hernandez-Bermejo, Benito .
PHYSICA D-NONLINEAR PHENOMENA, 2010, 239 (17) :1665-1669
[37]   BIFURCATION OF LIMIT CYCLES BY PERTURBING A PERIODIC ANNULUS WITH MULTIPLE CRITICAL POINTS [J].
Chang, Guifeng ;
Han, Maoan .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2013, 23 (08)
[38]   Bifurcation of limit cycles from a non-smooth perturbation of a two-dimensional isochronous cylinder [J].
Buzzi, C. A. ;
Euzebio, R. D. ;
Mereu, A. C. .
BULLETIN DES SCIENCES MATHEMATIQUES, 2016, 140 (05) :519-540
[39]   NEW METHOD FOR THE ELIMINATION OF 2-DIMENSIONAL LIMIT-CYCLES IN 1ST ORDER STRUCTURES [J].
MCLERNON, DC .
IEE PROCEEDINGS-G CIRCUITS DEVICES AND SYSTEMS, 1991, 138 (05) :541-550
[40]   Bifurcation of limit cycles in piecewise-smooth systems with intersecting discontinuity surfaces [J].
Hosham, Hany A. .
NONLINEAR DYNAMICS, 2020, 99 (03) :2049-2063
12345