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Bursting Oscillations in Shimizu-Morioka System with Slow-Varying Periodic Excitation
Joint Authors
Source
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-03-14
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Ma, Xindong& Cao, Shuqian. 2018. Bursting Oscillations in Shimizu-Morioka System with Slow-Varying Periodic Excitation. Shock and Vibration،Vol. 2018, no. 2018, pp.1-11.
https://search.emarefa.net/detail/BIM-1215309
Modern Language Association (MLA)
Ma, Xindong& Cao, Shuqian. Bursting Oscillations in Shimizu-Morioka System with Slow-Varying Periodic Excitation. Shock and Vibration No. 2018 (2018), pp.1-11.
https://search.emarefa.net/detail/BIM-1215309
American Medical Association (AMA)
Ma, Xindong& Cao, Shuqian. Bursting Oscillations in Shimizu-Morioka System with Slow-Varying Periodic Excitation. Shock and Vibration. 2018. Vol. 2018, no. 2018, pp.1-11.
https://search.emarefa.net/detail/BIM-1215309
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1215309