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A Method to Determine Oscillation Emergence Bifurcation in Time-Delayed LTI System with Single Lag.
- Source :
-
Journal of Applied Mathematics . 2014, p1-12. 12p. - Publication Year :
- 2014
-
Abstract
- 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 oscillationmode will emerge. Next, amethod to determine OEB bifurcation in the timedelayed LTI system with single lag is developed based on LambertWfunction. 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BIFURCATION theory
*TIME delay systems
*LINEAR systems
*EIGENVALUES
*OSCILLATIONS
Subjects
Details
- Language :
- English
- ISSN :
- 1110757X
- Database :
- Academic Search Index
- Journal :
- Journal of Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 100493499
- Full Text :
- https://doi.org/10.1155/2014/823937