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

Xiaodan Yu | Zendy; Hongjie Jia | Zendy; Wang Chengshan | Zendy; Yilang Jiang | Zendy

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

Author(s) -

Xiaodan Yu,

Hongjie Jia,

Wang Chengshan,

Yilang Jiang

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/823937

Subject(s) - bifurcation , eigenvalues and eigenvectors , oscillation (cell signaling) , control theory (sociology) , correctness , mathematics , saddle node bifurcation , lti system theory , stability (learning theory) , mathematical analysis , physics , linear system , computer science , nonlinear system , chemistry , algorithm , biochemistry , control (management) , quantum mechanics , artificial intelligence , machine learning

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

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