Generalized Hopf bifurcation of a non-smooth railway wheelset system

Release time:2020-07-02

DOI number:10.1007/s11071-020-05702-7

Journal:Nonlinear Dynamics

Key Words:Wheelset; Center manifold theorem; Generalized Hopf bifurcation; Poincare map; ́Non- smooth system

Abstract:In this paper, we investigate the general- ized Hopf bifurcation of a non-smooth railway wheelset system. It is to note that the system is a four-dimensional non-smooth differential equation. First, we show how to overcome the non-smoothness and reduce the four-dimensional system to a two- dimensional non-smooth system by the center mani- fold theorem. Since the two-dimensional central manifold is still non-smooth, we cannot apply the classical Hopf bifurcation theorem. Hence, we need to construct and analyze a Poincare ́ map so that a criterion for determining the generalized Hopf bifur- cation occurring in the system is given. Finally, to demonstrate our theoretical results, we also give some numerical simulations which are presented to exhibit the corresponding bifurcation diagrams.

Co-author:Li Denghui, Yue Yuan, Xie Jianhua

First Author:Miao Pengcheng

Indexed by:Journal paper

Correspondence Author:Chen Hebai

Discipline:力学

Document Type:J

Volume:100

Page Number:3277-3293

Translation or Not:no

Date of Publication:2020-07-01

Links to published journals:https://doi.org/10.1007/s11071-020-05702-7