Periodic flows to chaos in time-delay systems / Albert C.J. Luo.
Luo, Albert C. J.
2016
TJ216
Available Online

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Title Periodic flows to chaos in time-delay systems / Albert C.J. Luo.
Author Luo, Albert C. J.
ISBN 9783319426648 (electronic book)
3319426648 (electronic book)
9783319426631
331942663X
Publication Details Switzerland : Springer, 2016, ©2017.
Language English
Description 1 online resource.
Call Number TJ216
Dewey Decimal Classification 629.8/3
620
Summary This book for the first time examines periodic motions to chaos in time-delay systems, which exist extensively in engineering. For a long time, the stability of time-delay systems at equilibrium has been of great interest from the Lyapunov theory-based methods, where one cannot achieve the ideal results. Thus, time-delay discretization in time-delay systems was used for the stability of these systems. In this volume, Dr. Luo presents an accurate method based on the finite Fourier series to determine periodic motions in nonlinear time-delay systems. The stability and bifurcation of periodic motions are determined by the time-delayed system of coefficients in the Fourier series and the method for nonlinear time-delay systems is equivalent to the Laplace transformation method for linear time-delay systems. Facilitates discovery of analytical solutions of nonlinear time-delay systems; Illustrates bifurcation trees of periodic motions to chaos; Helps readers identify motion complexity and singularity; Explains procedures for determining stability, bifurcation and chaos.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Series Nonlinear systems and complexity ; v. 16.
Available in Other Form Print version: 331942663X
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Preface; Contents; 1 Linear Time-Delay Systems and Stability; 1.1 Linear Time-Delay Systems; 1.2 Stability and Boundary; 1.3 Lower-Dimensional Linear Time-Delay Systems; 1.3.1 1-D Linear Time-Delay Systems; 1.3.2 2-D Linear Time-Delay Systems; 1.3.3 3-D Linear Time-Delay Systems; 2 Nonlinear Time-Delay Systems; 2.1 Time-Delay Continuous Systems; 2.2 Equilibriums and Stability; 2.3 Bifurcation and Stability Switching; 2.3.1 Stability and Switching; 2.3.2 Bifurcations; References; 3 Periodic Flows in Time-Delay Systems; 3.1 Autonomous Time-Delay Systems; 3.2 Non-Autonomous Time-Delay Systems.

3.3 Time-Delay, Free Vibration Systems3.4 Periodically Forced, Time-Delay Vibration Systems; Reference; 4 Quasi-periodic Flows in Time-Delay Systems; 4.1 Time-Delay Nonlinear Systems; 4.2 Time-Delay Nonlinear Vibration Systems; Reference; 5 Time-Delay Duffing Oscillators; 5.1 Analytical Solutions; 5.2 Period-1 Motions to Chaos; 5.2.1 Frequency-Amplitude Characteristics; 5.2.2 Period-1 to Period-4 Motions; 5.3 Period-3 Motions to Chaos; 5.3.1 Frequency-Amplitude Characteristics; 5.3.2 Period-3 and Period-6 Motions; References; Subject Index.

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