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A Linear Estimate of the Number of Limit Cycles for A Piecewise Smooth Near-Hamiltonian System

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Abstract

In this paper, we study Poincaré bifurcation of limit cycles from a piecewise linear Hamiltonian system with a center at the origin and a homoclinic loop round the origin. By using the Melnikov function method, we give an estimation of the number of limit cycles which bifurcate from the period annulus between the center and the homoclinic loop under the piecewise polynomial perturbations of degree n. This result confirms a conjecture.

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Authors and Affiliations

  1. College of Teacher Eduction, Zhejiang Normal University, Zhejiang, 321004, People’s Republic of China

    Xiaoyan Chen

  2. College of Science, Central South University of Forestry and Technology, Changsha, 410004, People’s Republic of China

    Xiaoyan Chen

  3. Department of Mathematics, Zhejiang Normal University, Zhejiang, 321004, People’s Republic of China

    Maoan Han

Authors
  1. Xiaoyan Chen
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  2. Maoan Han
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Correspondence to Maoan Han.

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Funding

This study was funded by National Natural Science Foundation of China (Nos. 11931016 and 11771296), Hunan Province Natural Science Foundation (No. 2018JJ3866), School Youth Foundation of Central South University of Forestry and Technology (No. QJ2017012B), Post Doctor Start-up Foundation of Zhejiang Normal University (No. ZC304019016).

Conflict of interest

Xiaoyan Chen declares that she has no conflict of interest. Maoan Han declares that he has no conflict of interest.

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Chen, X., Han, M. A Linear Estimate of the Number of Limit Cycles for A Piecewise Smooth Near-Hamiltonian System. Qual. Theory Dyn. Syst. 19, 61 (2020). https://doi.org/10.1007/s12346-020-00398-x

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  • DOI: https://doi.org/10.1007/s12346-020-00398-x

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