Year: 2020
Author: Qianqian Jia, Weipeng Zhang, Qiuying Lu, Xiaodong Li
Journal of Nonlinear Modeling and Analysis, Vol. 2 (2020), Iss. 1 : pp. 25–44
Abstract
In this work, bifurcation analysis near double homoclinic loops with $W^s$ inclination flip of $Γ_1$ and nonresonant eigenvalues is presented in a four-dimensional system. We establish a Poincaré map by constructing local active coordinates approach in some tubular neighborhood of unperturbed double homoclinic loops. Through studying the bifurcation equations, we obtain the condition that the original double homoclinic loops are persistent, and get the existence or the nonexistence regions of the large 1-homoclinic orbit and the large 1-periodic orbit. At last, an analytical example is given to illustrate our main results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2020.25
Journal of Nonlinear Modeling and Analysis, Vol. 2 (2020), Iss. 1 : pp. 25–44
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Double homoclinic loops Nonresonant eigenvalues Inclination flip Periodic orbit Bifurcation.