Bifurcations of Double Homoclinic Loops in Reversible Systems

Author:

Bai Yuzhen1,Liu Xingbo2ORCID

Affiliation:

1. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, P. R. China

2. Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, P. R. China

Abstract

This paper is devoted to the study of bifurcation phenomena of double homoclinic loops in reversible systems. With the aid of a suitable local coordinate system, the Poincaré map is constructed. By means of the bifurcation equation, we perform a detailed study to obtain fruitful results, and demonstrate the existence of the R-symmetric large homoclinic orbit of new type near the primary double homoclinic loops, the existence of infinitely many R-symmetric periodic orbits accumulating onto the R-symmetric large homoclinic orbit, and the coexistence of R-symmetric large homoclinic orbit and the double homoclinic loops. The homoclinic bellow can also be found under suitable perturbation. The relevant bifurcation surfaces and the existence regions are located.

Funder

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. BIFURCATIONS OF TWISTED FINE HETEROCLINIC LOOP FOR HIGH-DIMENSIONAL SYSTEMS;Journal of Applied Analysis & Computation;2023

2. Homoclinic orbits in three-dimensional continuous piecewise linear generalized Michelson systems;Chaos: An Interdisciplinary Journal of Nonlinear Science;2022-07

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