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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2014-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/95/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |