Applied Mathematics and Nonlinear Sciences
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Journal

Applied Mathematics and Nonlinear Sciences


Volume
& Issue

Volume 9, Issue 1


Published
on

February 15, 2024


Pages


DOI

Article

Pitchfork bifurcation and vibrational resonance in a neutral delayed system

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Authors

Bin Zhang Affiliation:
Department of Mechanical Engineering, Shanxi Engineering Vocational College, Taiyuan, 030009, China.


Abstract

The pitchfork bifurcation and vibrational resonance phenomenon are analytically and numerically investigated in the neutral delayed system. The results show that the neutral delayed time induces the pitchfork bifurcation transiting between supercritical and subcritical cases while the neutral delayed strength may induce supercritical pitchfork bifurcation. The neutral delayed time can also induce the periodic or quasi-periodic vibrational resonance. This period simultaneously contains the period of the low-frequency harmonic excitation and period of the high-frequency harmonic excitation. The results extend the investigations of the pitchfork bifurcation and vibrational resonance.


Keywords

Neutral delayed time, pitchfork bifurcation, vibrational resonance, 70K70


Citation

Zhang, B. (2024). Pitchfork bifurcation and vibrational resonance in a neutral delayed system. Applied Mathematics and Nonlinear Sciences, 9(1). https://doi.org/10.2478/amns-2024-0012

Published by: Engineering Journals

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