Bifurcation Analysis and Spatiotemporal Patterns in Unidirectionally Delay-Coupled Vibratory Gyroscopes

被引:3
作者
Li, Li [1 ]
Xu, Jian [1 ]
机构
[1] Tongji Univ, Sch Aerosp Engn & Appl Mech, Shanghai 200092, Peoples R China
来源
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2018年 / 28卷 / 02期
基金
中国国家自然科学基金;
关键词
Vibratory gyroscope; unidirectional coupling; time delay; Hopf bifurcation; spatio-temporal patterns; FUNCTIONAL-DIFFERENTIAL EQUATIONS; HOPF-BIFURCATION; NORMAL FORMS; SYSTEMS; SYNCHRONIZATION;
D O I
10.1142/S0218127418500293
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Time delay is inevitable in unidirectionally coupled drive-free vibratory gyroscope system. The effect of time delay on the gyroscope system is studied in this paper. To this end, amplitude death and Hopf bifurcation induced by small time delay are first investigated by analyzing the related characteristic equation. Then, the direction of Hopf bifurcations and stability of Hopf-bifurcating periodic oscillations are determined by calculating the normal form on the center manifold. Next, spatiotemporal patterns of these Hopf-bifurcating periodic oscillations are analyzed by using the symmetric bifurcation theory of delay differential equations. Finally, it is found that numerical simulations agree with the associated analytic results. These phenomena could be induced although time delay is very small. Therefore, it is shown that time delay is an important factor which influences the sensitivity and accuracy of the gyroscope system and cannot be neglected during the design and manufacture.
引用
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页数:14
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