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

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.

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Main Authors: Minzhi Wei, Junning Cai, Hongying Zhu
Format: Article
Language:English
Published: Wiley 2019-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2019/6943563
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author Minzhi Wei
Junning Cai
Hongying Zhu
author_facet Minzhi Wei
Junning Cai
Hongying Zhu
author_sort Minzhi Wei
collection DOAJ
description 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.
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institution Kabale University
issn 1026-0226
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publishDate 2019-01-01
publisher Wiley
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series Discrete Dynamics in Nature and Society
spelling doaj-art-491ce89c35b74cafba9288c8d1fbcb632025-08-20T03:36:47ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2019-01-01201910.1155/2019/69435636943563Poincaré Bifurcation of Limit Cycles from a Liénard System with a Homoclinic Loop Passing through a Nilpotent SaddleMinzhi Wei0Junning Cai1Hongying Zhu2Department of Applied Mathematics, Guangxi University of Finance and Economics, Nanning, Guangxi, 530003, ChinaDepartment of Applied Mathematics, Guangxi University of Finance and Economics, Nanning, Guangxi, 530003, ChinaDepartment of Applied Mathematics, Guangxi University of Finance and Economics, Nanning, Guangxi, 530003, ChinaIn 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.http://dx.doi.org/10.1155/2019/6943563
spellingShingle Minzhi Wei
Junning Cai
Hongying Zhu
Poincaré Bifurcation of Limit Cycles from a Liénard System with a Homoclinic Loop Passing through a Nilpotent Saddle
Discrete Dynamics in Nature and Society
title Poincaré Bifurcation of Limit Cycles from a Liénard System with a Homoclinic Loop Passing through a Nilpotent Saddle
title_full Poincaré Bifurcation of Limit Cycles from a Liénard System with a Homoclinic Loop Passing through a Nilpotent Saddle
title_fullStr Poincaré Bifurcation of Limit Cycles from a Liénard System with a Homoclinic Loop Passing through a Nilpotent Saddle
title_full_unstemmed Poincaré Bifurcation of Limit Cycles from a Liénard System with a Homoclinic Loop Passing through a Nilpotent Saddle
title_short Poincaré Bifurcation of Limit Cycles from a Liénard System with a Homoclinic Loop Passing through a Nilpotent Saddle
title_sort poincare bifurcation of limit cycles from a lienard system with a homoclinic loop passing through a nilpotent saddle
url http://dx.doi.org/10.1155/2019/6943563
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AT junningcai poincarebifurcationoflimitcyclesfromalienardsystemwithahomocliniclooppassingthroughanilpotentsaddle
AT hongyingzhu poincarebifurcationoflimitcyclesfromalienardsystemwithahomocliniclooppassingthroughanilpotentsaddle