| Popis: |
This paper first investigates all possible phase portraits of a class of planar quintic vector field given by x ˙ = ( 1 + 2 b x 2 + 2 d x 4 ) y , y ˙ = − 2 ( 2 a x 2 + b y 2 + 3 c x 4 + 2 d x 2 y 2 ) x , a , b , c , d ∈ R . Then, we study the bifurcation problem of its small perturbed vector field with polynomial perturbations of arbitrary degree n , n ∈ N by the corresponding Abelian integral, and prove that the lower bound for the maximal number of limit cycles bifurcating from the periodic orbits is 3 [ n − 1 2 ] − 1 , n ≥ 5 . |
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