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Poincaré Bifurcation from an Elliptic Hamiltonian of Degree Four with Two-Saddle Cycle

Poincaré Bifurcation from an Elliptic Hamiltonian of Degree Four with Two-Saddle Cycle

Year:    2022

Author:    Yu’e Xiong, Wenyu Li, Qinlong Wang

Journal of Nonlinear Modeling and Analysis, Vol. 4 (2022), Iss. 4 : pp. 722–735

Abstract

In this paper, we consider Poincaré bifurcation from an elliptic Hamiltonian of degree four with two-saddle cycle. Based on the Chebyshev criterion, not only one case in the Liénard equations of type (3, 2) is discussed again in a different way from the previous ones, but also its two extended cases are investigated, where the perturbations are given respectively by adding εy(d0+d2v2n)y with nN+ and εy(d0+d4v4+d2v2n+4)y with n=1 or nN+, for small ε>0. For the above cases, we obtain all the sharp upper bound of the number of zeros for Abelian integrals, from which the existence of limit cycles at most via the first-order Melnikov functions is determined. Finally, one example of double limit cycles for the latter case is given.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.12150/jnma.2022.722

Journal of Nonlinear Modeling and Analysis, Vol. 4 (2022), Iss. 4 : pp. 722–735

Published online:    2022-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    Perturbed Hamiltonian system Poincaré bifurcation Abelian integral Chebyshev criterion.

Author Details

Yu’e Xiong Email

Wenyu Li Email

Qinlong Wang Email