Abstract
In this paper, we show that generic planar quadratic Hamiltonian systems with third degree polynomial perturbation can have eight small-amplitude limit cycles around a center. We use higher-order focus value computation to prove this result, which is equivalent to the computation of higher-order Melnikov functions. Previous results have shown, based on first-order and higher-order Melnikov functions, that planar quadratic Hamiltonian systems with third degree polynomial perturbation can have five or seven small-amplitude limit cycles around a center. The result given in this paper is a further improvement.
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