Sliding Homoclinic Bifurcations in a Class of Three-Dimensional Piecewise Affine Systems-Reference-Cited by-同舟云学术

Sliding Homoclinic Bifurcations in a Class of Three-Dimensional Piecewise Affine Systems

Published:2024-07 Issue:09 Volume:34 Page:
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Wu Tiantian¹^ORCID,Zhao Zhe¹^ORCID,Huan Songmei²^ORCID

Affiliation:

1. School of Mathematics and Statistics, Shandong Normal University, Ji’nan 250014, P. R. China

2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Wuhan 430074, P. R. China

Abstract

This paper studies sliding homoclinic bifurcations in a class of symmetric three-zone three-dimensional piecewise affine systems. The systems have one parameter and the unperturbed systems have a pair of sliding homoclinic orbits to a saddle. Based on the analysis of the one-dimensional Poincaré maps, two types of sliding cycles are obtained from the sliding homoclinic bifurcations of the systems. In addition, two examples of sliding homoclinic orbits and sliding cycles are provided with simulations to illustrate the effectiveness of the theorems.

Funder

National Natural Science Foundation of China

Natural Science Foundation of Shandong Province

Publisher

World Scientific Pub Co Pte Ltd

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127424300192

Reference32 articles.

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