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ON THE NUMBER OF LIMIT CYCLES IN NEAR-HAMILTONIAN POLYNOMIAL SYSTEMS.
- Source :
- International Journal of Bifurcation & Chaos in Applied Sciences & Engineering; Jun2007, Vol. 17 Issue 6, p2033-2047, 15p, 2 Graphs
- Publication Year :
- 2007
-
Abstract
- In this paper we study a general near-Hamiltonian polynomial system on the plane. We suppose the unperturbed system has a family of periodic orbits surrounding a center point and obtain some sufficient conditions to find the cyclicity of the perturbed system at the center or a periodic orbit. In particular, we prove that for almost all polynomial Hamiltonian systems the perturbed systems with polynomial perturbations of degree n have at most n(n + 1)/2 - 1 limit cycles near a center point. We also obtain some new results for Lienard systems by applying our main theorems. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02181274
- Volume :
- 17
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 26431227
- Full Text :
- https://doi.org/10.1142/S0218127407018208