### Abstract

In this paper we study the limit cycles of the system over(x, ̇) = - y (x + a) (y + b) + ε P (x, y), over(y, ̇) = x (x + a) (y + b) + ε Q (x, y) for ε sufficiently small, where a, b ∈ R {minus 45 degree rule} {0}, and P, Q are polynomials of degree n. We obtain that 3[(n - 1)/2] + 4 if a ≠ b and, respectively, 2[(n - 1)/2] + 2 if a = b, up to first order in ε, are upper bounds for the number of the limit cycles that bifurcate from the period annulus of the cubic center given by ε = 0. Moreover, there are systems with at least 3[(n - 1)/2] + 2 limit cycles if a ≠ b and, respectively, 2[(n - 1)/2] + 1 if a = b. © 2005 Elsevier Ltd. All rights reserved.

Original language | English |
---|---|

Pages (from-to) | 1059-1069 |

Journal | Chaos, Solitons and Fractals |

Volume | 32 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 May 2007 |

## Fingerprint Dive into the research topics of 'Limit cycles of a perturbed cubic polynomial differential center'. Together they form a unique fingerprint.

## Cite this

Buicǎ, A., & Llibre, J. (2007). Limit cycles of a perturbed cubic polynomial differential center.

*Chaos, Solitons and Fractals*,*32*(3), 1059-1069. https://doi.org/10.1016/j.chaos.2005.11.060