Improves count of limit cycles in near-Hamiltonian systems, suggesting broader applicability of a new method.
For a kind of near-Hamiltonian systems of degree [Formula: see text] subject to polynomial perturbations, we improve the existing results on the number of limit cycles near a homoclinic loop with a cusp. More significantly, the new method for calculating coefficients in the expansion of the first-order Melnikov function can be extended to many other cases.
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Yang et al. (2026) studied this question.
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