A Method to Determine Oscillation Emergence Bifurcation in Time-Delayed LTI System with Single Lag

Yu Xiaodan, Jia Hongjie, Wang Chengshan and Jiang Yilang

Journal of Applied Mathematics, 2014, vol. 2014, 1-12

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 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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:823937

DOI: 10.1155/2014/823937

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