| Description |
1 online resource |
| Series |
Nonlinear systems and complexity, 2195-9994 ; volume 16 |
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Nonlinear systems and complexity ; v. 16.
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| Contents |
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 |
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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 |
| 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 |
Includes bibliographical references and index |
| Subject |
Time delay systems.
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Chaotic behavior in systems.
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TECHNOLOGY & ENGINEERING -- Engineering (General)
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Chaotic behavior in systems
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Time delay systems
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| Form |
Electronic book
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| ISBN |
9783319426648 |
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3319426648 |
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