A Method to Determine Oscillation Emergence Bifurcation in Time-Delayed LTI System with Single Lag
| Autor: | Yu Xiaodan, Jia Hongjie, Wang Chengshan, Jiang Yilang |
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| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Journal of Applied Mathematics, Vol 2014 (2014) |
| Druh dokumentu: | article |
| ISSN: | 1110-757X 1687-0042 |
| DOI: | 10.1155/2014/823937 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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