Bursting Oscillations in Shimizu-Morioka System with Slow-Varying Periodic Excitation

The coupling effect of two different frequency scales between the exciting frequency and the natural frequency of the Shimizu-Morioka system with slow-varying periodic excitation is investigated. First, based on the analysis of the equilibrium states, homoclinic bifurcation, fold bifurcation, and su...

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Bibliographic Details
Main Authors: Xindong Ma, Shuqian Cao
Format: Article
Language:English
Published: Wiley 2018-01-01
Series:Shock and Vibration
Online Access:http://dx.doi.org/10.1155/2018/5207910
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Summary:The coupling effect of two different frequency scales between the exciting frequency and the natural frequency of the Shimizu-Morioka system with slow-varying periodic excitation is investigated. First, based on the analysis of the equilibrium states, homoclinic bifurcation, fold bifurcation, and supercritical Hopf bifurcation are observed in the system under a certain parameter condition. When the exciting frequency is much smaller than the natural frequency, we can regard the periodic excitation as a slow-varying parameter. Second, complicated dynamic behaviors are analyzed when the slow-varying parameter passes through different bifurcation points, of which the mechanisms of four different bursting patterns, namely, symmetric “homoclinic/homoclinic” bursting oscillation, symmetric “fold/Hopf” bursting oscillation, symmetric “fold/fold” bursting oscillation, and symmetric “Hopf/Hopf” bursting oscillation via “fold/fold” hysteresis loop, are revealed with different values of the parameter b by means of the transformed phase portrait. Finally, we can find that the time interval between two symmetric adjacent spikes of bursting oscillations exhibits dependency on the periodic excitation frequency.
ISSN:1070-9622
1875-9203