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Bifurcation of Limit Cycles from a Non-Hamiltonian Quadratic Integrable System with Homoclinic Loop

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Infinite Dimensional Dynamical Systems

Part of the book series: Fields Institute Communications ((FIC,volume 64))

Abstract

In this chapter, we study quadratic perturbations of a non-Hamiltonian quadratic integrable system with a homoclinic loop. We prove that the perturbed system has at most two limit cycles in the finite phase plane, and the bound is exact. The proof relies on an estimation of the number of zeros of related Abelian integrals.

Mathematics Subject Classification 2010(2010): Primary 34C05,34C25,34C27; Secondary

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Acknowledgements

Zhao was partially supported by NSF of China (No. 11171355) and the Program for New Century Excellent Talents of Universities of China.This research of Zhu was supported by Natural Sciences and Engineering Research Council (NSERC) of Canada.

Received 8/16/2010; Accepted 10/10/2011

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Authors and Affiliations

  1. Department of Mathematics, School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou, 510275, P.R. China

    Yulin Zhao

  2. Department of Mathematics and Statistics, York University, Toronto, ON, Canada, M3J 1P3

    Huaiping Zhu

Authors
  1. Yulin Zhao
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  2. Huaiping Zhu
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Corresponding author

Correspondence to Yulin Zhao .

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Editors and Affiliations

  1. Division of Applied Mathematics, Brown University, Providence, RI, USA

    John Mallet-Paret

  2. Department of Mathematics and Statistics, York University, Toronto, ON, Canada

    Jianhong Wu  & Huaiping Zhu  & 

  3. Georgia Institute of Technology, School of Mathematics, Atlanta, GA, USA

    Yingfei Yi

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Zhao, Y., Zhu, H. (2013). Bifurcation of Limit Cycles from a Non-Hamiltonian Quadratic Integrable System with Homoclinic Loop. In: Mallet-Paret, J., Wu, J., Yi, Y., Zhu, H. (eds) Infinite Dimensional Dynamical Systems. Fields Institute Communications, vol 64. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4523-4_18

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