Bifurcation analysis of the bogie system with time delay and the influence of parameters on the system

Abstract

In this paper, a bogie system with time delay is established. The centre manifold theorem and norm form theory are used to reduce the infinite dimensional delay system to the finite dimensional ordinary differential system, and the bifurcation behaviour of the bogie system is analysed. The MatCont toolkit was used to verify the subcritical bifurcation in the system. In addition, the influence of parameters on the bifurcation diagram of the system and the influence of parameters on the critical speed of the bogie system during the hunting motion are also analysed.

Keywords:

• Time delay
• bogie system
• bifurcation
• hunting motion

Acknowledgments

All authors contributed to the study, conception, and design. Analysis was performed by XZ, YL, SY, YL and PW. The first draft of the manuscript was written by XY and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Disclosure statement

The authors declared that they have no conflicts of interest to this work. We do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. The work described has not been submitted elsewhere for publication, in whole or in part, and all the authors listed have approved the manuscript that is enclosed.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant numbers 11790282, 12172235, 12072208 and 52072249], and the Opening Foundation of State Key Laboratory of Shijiazhuang Tiedao University [grant number ZZ2021-13] and the Project for Postgraduate Innovation Ability Training Subsidy of Shijiazhuang Tiedao University [grant numbers YC2023002].