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- Title
Bifurcation of Limit Cycles from a Quintic Center via the Second Order Averaging Method.
- Authors
Peng, Linping; Feng, Zhaosheng
- Abstract
This paper is concerned with the bifurcation of limit cycles from a quintic system with one center. By using the averaging theory, we show that under any small quintic homogeneous perturbations, up to order 1 in ε, at most three limit cycles bifurcate from periodic orbits of the considered system, and this upper bound can be reached. Up to order 2 in ε, at most seven limit cycles emerge from periodic orbits of the unperturbed one.
- Subjects
BIFURCATION theory; LIMIT cycles; QUINTIC curves; AVERAGING method (Differential equations); PERTURBATION theory
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2015, Vol 25, Issue 3, p-1
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127415500479