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Article Contents

# A new cubic system having eleven limit cycles

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

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