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Discrete Dynamics in Nature and Society
Volume 2019, Article ID 6943563, 12 pages
Research Article

Poincaré Bifurcation of Limit Cycles from a Liénard System with a Homoclinic Loop Passing through a Nilpotent Saddle

Department of Applied Mathematics, Guangxi University of Finance and Economics, Nanning, Guangxi, 530003, China

Correspondence should be addressed to Minzhi Wei; moc.361@321gnoixnayoaix

Received 22 February 2019; Accepted 14 May 2019; Published 2 June 2019

Academic Editor: Douglas R. Anderson

Copyright © 2019 Minzhi Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In present paper, the number of zeros of the Abelian integral is studied, which is for some perturbed Hamiltonian system of degree 6. We prove the generating elements of the Abelian integral from a Chebyshev system of accuracy of 3; therefore there are at most 6 zeros of the Abelian integral.