A new cubic system having eleven limit cycles

Maoan Han; Yuhai Wu; Ping Bi

doi:10.3934/dcds.2005.12.675

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2005, Volume 12, Issue 4: 675-686. Doi: 10.3934/dcds.2005.12.675

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A new cubic system having eleven limit cycles

1.
Department of Mathematics, Shanghai Normal University, Shanghai 200234
2.
Department of Mathematics, Shanghai Normal University, Tempe, Shanghai 200234

Received: August 31, 2003

Revised: October 31, 2004

Published: June 2005

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Abstract

This paper concerns with the number and distribution of limit cycles of a perturbed cubic Hamiltonian system which has 5 centers and 4 saddle points. The stability analysis and bifurcation methods of differential equations are applied to study the homoclinic loop bifurcation under $Z_2$-equivariant cubic perturbation. It is proved that the perturbed system can have 11 limit cycles with two different distributions, one of which is already known, the other is new.

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Mathematics Subject Classification: 34G10, 47D06, 58F11, 92D25.

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