Cluster vibration and bifurcation of a fractional-order Brusselator oscillator

被引：0
|
作者：
Wang Y. [1 ]
Li X. [1 ,2 ,3 ]
Wang M. [2 ]
Shen Y. [1 ,3 ]
机构：
[1] School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang
[2] Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang
[3] State Key Lab of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang
来源：
Zhendong yu Chongji/Journal of Vibration and Shock | 2022年 / 41卷 / 08期
关键词：
Brusselator oscillator; Cluster vibration; Factional order system; Slow-fast analysis method;
D O I：
10.13465/j.cnki.jvs.2022.08.037
中图分类号：
学科分类号：
摘要：
A Brusselator oscillator is a typical multi-scale coupling system because of catalyst, which will lead to cluster vibration behavior, characterized by the spiking state coupled with the quiescence state. In this paper, we consider the fractional-order Brusselator system under external periodic disturbance, and the nonlinear behaviors of the system are more complex. Based on the stability theory of a fractional order system, the two-parameter bifurcation analysis was carried out, and the sufficient conditions of Hopf bifurcation were discussed. It was found that there is a singular line in the system, and its stability was verified by using the center manifold theorem and numerical simulation. The influence of different fractional orders on cluster vibration was discussed. Through the two-parameter bifurcation diagram with respect to fractional order and slowly varying parameters, it was found that the fractional order is closely related to the time of the spiking state. That is to say, reducing the fractional order of the system can shorten the time of the spiking state and increase the time of the quiescence state. It was also found that the variation of disturbance amplitude directly affects the type of the attractor of the fast subsystem. When the excitation amplitude is large, two kinds of attractors are involved in the fast subsystem, the quiescence state and the spiking state coexist. When the excitation amplitude is small, the fast subsystem involves one kind of the attractor, then the quiescence state disappears. © 2022, Editorial Office of Journal of Vibration and Shock. All right reserved.
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页码：304 / 310and322
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