Periodic Flows to Chaos in Time-delay Systems

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.

List of contents

Linear Time-delay Systems.- Nonlinear Time-delay System.- Periodic Flows in Time-delay Systems.- Quasiperiodic Flows in Time-delay Systems.- Time-delay Duffing Oscillator.

About the author

Dr. Albert C. J. Luo is Professor of Mechanical Engineering at Southern Illinois University in Edwardsville.

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.

Product details

• Authors: Albert C J Luo, Albert C. J. Luo
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2018
• EAN: 9783319826318
• ISBN: 978-3-31-982631-8
• No. of pages: 198
• Dimensions: 155 mm x 11 mm x 235 mm
• Weight: 326 g
• Illustrations: X, 198 p. 30 illus., 15 illus. in color.
• Series: Nonlinear Systems and Complexity; Nonlinear Systems and Complexity
• Subjects: Natural sciences, medicine, IT, technology > Technology > General, dictionaries; B, Optische Physik, engineering, complexity, Complex systems, Nonlinear science, Applied mathematics, System Theory, Dynamics & statics, Applications of Nonlinear Dynamics and Chaos Theory, Statistical physics, Nonlinear Optics, Applied Dynamical Systems, Computational complexity