A Method to Determine Oscillation Emergence Bifurcation in Time-Delayed LTI System with Single Lag
Joint Authors
Xiaodan, Yu
Yilang, Jiang
Jia, Hongjie
Wang, Cheng-shan
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-07-03
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
One type of bifurcation named oscillation emergence bifurcation (OEB) found in time-delayed linear time invariant (abbr.
LTI) systems is fully studied.
The definition of OEB is initially put forward according to the eigenvalue variation.
It is revealed that a real eigenvalue splits into a pair of conjugated complex eigenvalues when an OEB occurs, which means the number of the system eigenvalues will increase by one and a new oscillation mode will emerge.
Next, a method to determine OEB bifurcation in the time-delayed LTI system with single lag is developed based on Lambert W function.
A one-dimensional (1-dim) time-delayed system is firstly employed to explain the mechanism of OEB bifurcation.
Then, methods to determine the OEB bifurcation in 1-dim, 2-dim, and high-dimension time-delayed LTI systems are derived.
Finally, simulation results validate the correctness and effectiveness of the presented method.
Since OEB bifurcation occurs with a new oscillation mode emerging, work of this paper is useful to explore the complex phenomena and the stability of time-delayed dynamic systems.
American Psychological Association (APA)
Xiaodan, Yu& Jia, Hongjie& Wang, Cheng-shan& Yilang, Jiang. 2014. A Method to Determine Oscillation Emergence Bifurcation in Time-Delayed LTI System with Single Lag. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-501009
Modern Language Association (MLA)
Xiaodan, Yu…[et al.]. A Method to Determine Oscillation Emergence Bifurcation in Time-Delayed LTI System with Single Lag. Journal of Applied Mathematics No. 2014 (2014), pp.1-12.
https://search.emarefa.net/detail/BIM-501009
American Medical Association (AMA)
Xiaodan, Yu& Jia, Hongjie& Wang, Cheng-shan& Yilang, Jiang. A Method to Determine Oscillation Emergence Bifurcation in Time-Delayed LTI System with Single Lag. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-501009
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-501009