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Periodic flows to chaos in time-dela...

Luo, Albert C.J.

Periodic flows to chaos in time-delay systems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Periodic flows to chaos in time-delay systemsby Albert C.J. Luo.
Author:	Luo, Albert C.J.
Published:	Cham :Springer International Publishing :2017.
Description:	x, 198 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Time delay systems.
Online resource:	http://dx.doi.org/10.1007/978-3-319-42664-8
ISBN:	9783319426648$q(electronic bk.)

Periodic flows to chaos in time-delay systems
Luo, Albert C.J.

Periodic flows to chaos in time-delay systems[electronic resource] /by Albert C.J. Luo. - Cham :Springer International Publishing :2017. - x, 198 p. :ill., digital ;24 cm. - Nonlinear systems and complexity,v.162195-9994 ;. - Nonlinear systems and complexity ;7..

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

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.

ISBN: 9783319426648$q(electronic bk.)

Standard No.: 10.1007/978-3-319-42664-8doiSubjects--Topical Terms:

239637
Time delay systems.

LC Class. No.: TJ216

Dewey Class. No.: 629.83

Periodic flows to chaos in time-delay systems
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520 $a 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.
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