Four limit cycles from perturbing quadratic integrable systems by quadratic polynomials

2010/02/04 by Pei Yu, Maoan Han, Yu, Pei +1
Mathematics · Medicine · Physics and Astronomy · #34C07 #34C23 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1002.1055

openalex publication_date 2010/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give a positive answer to the open question: Can there exist 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. The method of Melnikov function is used.

Citations

• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS

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