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Volume 1, Number 2, 2011, Pages 291-298                                                                DOI:10.11948/2011020
\( {\small \bf Communication Letter:}\) Four limit cycles in quadratic near-integrable system
Pei Yu,Maoan Han
Keywords:Hilbert’s 16th problem, quadratic near-integrable system, limit cycle, reversible system, Hopf bifurcation, Melnikov function.
      In this note, we report of obtaining 4 limit cycles in quadratic near-integrable polynomial systems. It is shown that when a quadratic integrable system has two centers and is perturbed by quadratic polynomials, it can generate at least 4 limit cycles with (3.1) distribution. This result provides a positive answer to an open problem in this area.
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