Bifurcation of limit cycles from quartic isochronous systems
This article concerns the bifurcation of limit cycles for a quartic system with an isochronous center. By using the averaging theory, it shows that under any small quartic homogeneous perturbations, at most two limit cycles bifurcate from the period annulus of the considered system, and this upp...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2014-04-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/95/abstr.html |
| _version_ | 1818355206162743296 |
|---|---|
| author | Linping Peng Zhaosheng Feng |
| author_facet | Linping Peng Zhaosheng Feng |
| author_sort | Linping Peng |
| collection | DOAJ |
| description | This article concerns the bifurcation of limit cycles for a quartic
system with an isochronous center. By using the averaging theory,
it shows that under any small quartic homogeneous perturbations,
at most two limit cycles bifurcate from the period annulus of the
considered system, and this upper bound can be reached.
In addition, we study a family of perturbed isochronous systems
and prove that there are at most three limit cycles
bifurcating from the period annulus of the unperturbed one, and the
upper bound is sharp. |
| first_indexed | 2024-12-13T19:37:38Z |
| format | Article |
| id | doaj.art-304757c7f3de49efb64e9b70aa39c564 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-13T19:37:38Z |
| publishDate | 2014-04-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-304757c7f3de49efb64e9b70aa39c5642022-12-21T23:33:46ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912014-04-01201495,114Bifurcation of limit cycles from quartic isochronous systemsLinping Peng0Zhaosheng Feng1 Beihang Univ., Beijing, China Univ. of Texas-Pan American, Edinburg, TX, USA This article concerns the bifurcation of limit cycles for a quartic system with an isochronous center. By using the averaging theory, it shows that under any small quartic homogeneous perturbations, at most two limit cycles bifurcate from the period annulus of the considered system, and this upper bound can be reached. In addition, we study a family of perturbed isochronous systems and prove that there are at most three limit cycles bifurcating from the period annulus of the unperturbed one, and the upper bound is sharp.http://ejde.math.txstate.edu/Volumes/2014/95/abstr.htmlBifurcationlimit cycleshomogeneous perturbationaveraging methodisochronous centerperiod annulus |
| spellingShingle | Linping Peng Zhaosheng Feng Bifurcation of limit cycles from quartic isochronous systems Electronic Journal of Differential Equations Bifurcation limit cycles homogeneous perturbation averaging method isochronous center period annulus |
| title | Bifurcation of limit cycles from quartic isochronous systems |
| title_full | Bifurcation of limit cycles from quartic isochronous systems |
| title_fullStr | Bifurcation of limit cycles from quartic isochronous systems |
| title_full_unstemmed | Bifurcation of limit cycles from quartic isochronous systems |
| title_short | Bifurcation of limit cycles from quartic isochronous systems |
| title_sort | bifurcation of limit cycles from quartic isochronous systems |
| topic | Bifurcation limit cycles homogeneous perturbation averaging method isochronous center period annulus |
| url | http://ejde.math.txstate.edu/Volumes/2014/95/abstr.html |
| work_keys_str_mv | AT linpingpeng bifurcationoflimitcyclesfromquarticisochronoussystems AT zhaoshengfeng bifurcationoflimitcyclesfromquarticisochronoussystems |