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July  2005, 12(4): 675-686. doi: 10.3934/dcds.2005.12.675

A new cubic system having eleven limit cycles

Maoan Han 1, , Yuhai Wu 2, and  Ping Bi 2,

1. 

Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2. 

Department of Mathematics, Shanghai Normal University, Tempe, Shanghai 200234, China, China

Received  September 2003 Revised  November 2004 Published  January 2005

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.
Keywords: Saddle connection, homoclinic loop, stability..
Mathematics Subject Classification: 34G10, 47D06, 58F11, 92D2.
Citation: Maoan Han, Yuhai Wu, Ping Bi. A new cubic system having eleven limit cycles. Discrete and Continuous Dynamical Systems, 2005, 12 (4) : 675-686. doi: 10.3934/dcds.2005.12.675
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