Cluster vibration and bifurcation of a fractional-order Brusselator oscillator
WANG Yanli1, LI Xianghong1, 2, 3, WANG Min2, SHEN Yongjun1,3
1.School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;
2.Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;
3.State Key Lab of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University, Shijiazhuang 050043, China
Abstract：The Brusselator oscillator is a typical multi-scale coupling system because of catalyst, which will lead to cluster vibration behavior, characterized by spiking state coupled with 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 fractional order system, the two-parameter bifurcation analysis is carried out, and the sufficient conditions of Hopf bifurcation are discussed. It is found that there is a singular line in the system, and its stability is verified by using the center manifold theorem and numerical simulation. The influence of different fractional orders on cluster vibration is discussed. Through the two-parameter bifurcation diagram with respect to fractional order and slowly varying parameters, it is 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 is also found that the variation of disturbance amplitude directly affects the type of 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 attractor, then the quiescence state disappears.
收稿日期: 2021-06-29
出版日期: 2022-04-28
引用本文:
王艳丽1，李向红1,2,3，王敏2，申永军1,3. 分数阶Brusselator振子的簇发振动与分岔[J]. 振动与冲击, 2022, 41(8): 304-310.
WANG Yanli1, LI Xianghong1, 2, 3, WANG Min2, SHEN Yongjun1,3. Cluster vibration and bifurcation of a fractional-order Brusselator oscillator. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(8): 304-310.
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