Four limit cycles from perturbing quadratic integrable systems by quadratic polynomials

摘要

In this paper, we give a positive answer to the open question: Can thereexist 4 limit cycles in quadratic near-integrable polynomial systems? It isshown that when a quadratic integrable system has two centers and is perturbedby quadratic polynomials, it can generate at least 4 limit cycles with (3,1)distribution. The method of Melnikov function is used.