FOUR LIMIT CYCLES IN QUADRATIC NEAR-INTEGRABLE SYSTEMS

Pei Yu; Maoan Han

doi:10.11948/2011020

2011 Volume 1 Issue 2

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Pei Yu, Maoan Han. FOUR LIMIT CYCLES IN QUADRATIC NEAR-INTEGRABLE SYSTEMS[J]. Journal of Applied Analysis & Computation, 2011, 1(2): 291-298. doi: 10.11948/2011020

Citation:

Pei Yu, Maoan Han. FOUR LIMIT CYCLES IN QUADRATIC NEAR-INTEGRABLE SYSTEMS[J]. Journal of Applied Analysis & Computation, 2011, 1(2): 291-298. doi: 10.11948/2011020

FOUR LIMIT CYCLES IN QUADRATIC NEAR-INTEGRABLE SYSTEMS

Pei Yu¹,
Maoan Han²

1 Department of Applied Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B7;
2 Department of Mathematics, Shanghai Normal University, Shanghai, 200234 China

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Abstract

Abstract

In this note, we report of obtaining 4 limit cycles in quadratic nearintegrable 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.
- Hilbert's 16th problem /
- quadratic near-integrable system /
- limit cycle /
- reversible system /
- Hopf bifurcation /
- Melnikov function
MSC: 34C07;34C23

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References

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