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Discretization and implicit mapping ...

Luo, Albert C.J.

Discretization and implicit mapping dynamics

Record Type:	Electronic resources : Monograph/item
Title/Author:	Discretization and implicit mapping dynamicsby Albert C.J. Luo.
Author:	Luo, Albert C.J.
Published:	Berlin, Heidelberg :Springer Berlin Heidelberg :2015.
Description:	x, 310 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Differential equations.
Online resource:	http://dx.doi.org/10.1007/978-3-662-47275-0
ISBN:	9783662472750 (electronic bk.)

Discretization and implicit mapping dynamics
Luo, Albert C.J.

Discretization and implicit mapping dynamics[electronic resource] /by Albert C.J. Luo. - Berlin, Heidelberg :Springer Berlin Heidelberg :2015. - x, 310 p. :ill., digital ;24 cm. - Nonlinear physical science,1867-8440. - Nonlinear physical science..

Introduction -- Nonlinear Discrete Systems -- Discretization of Continuous Systems -- Implicit Mapping Dynamics -- Periodic Flows in Continuous Systems -- Periodic Motions to Chaos in Duffing Oscillator.

This unique book presents the discretization of continuous systems and implicit mapping dynamics of periodic motions to chaos in continuous nonlinear systems. The stability and bifurcation theory of fixed points in discrete nonlinear dynamical systems is reviewed, and the explicit and implicit maps of continuous dynamical systems are developed through the single-step and multi-step discretizations. The implicit dynamics of period-m solutions in discrete nonlinear systems are discussed. The book also offers a generalized approach to finding analytical and numerical solutions of stable and unstable periodic flows to chaos in nonlinear systems with/without time-delay. The bifurcation trees of periodic motions to chaos in the Duffing oscillator are shown as a sample problem, while the discrete Fourier series of periodic motions and chaos are also presented. The book offers a valuable resource for university students, professors, researchers and engineers in the fields of applied mathematics, physics, mechanics, control systems, and engineering.

ISBN: 9783662472750 (electronic bk.)

Standard No.: 10.1007/978-3-662-47275-0doiSubjects--Topical Terms:

183925
Differential equations.

LC Class. No.: TA347.D45

Dewey Class. No.: 515.35

Discretization and implicit mapping dynamics
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245 1 0 $a Discretization and implicit mapping dynamics $h [electronic resource] / $c by Albert C.J. Luo.
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490 1 $a Nonlinear physical science, $x 1867-8440
505 0 $a Introduction -- Nonlinear Discrete Systems -- Discretization of Continuous Systems -- Implicit Mapping Dynamics -- Periodic Flows in Continuous Systems -- Periodic Motions to Chaos in Duffing Oscillator.
520 $a This unique book presents the discretization of continuous systems and implicit mapping dynamics of periodic motions to chaos in continuous nonlinear systems. The stability and bifurcation theory of fixed points in discrete nonlinear dynamical systems is reviewed, and the explicit and implicit maps of continuous dynamical systems are developed through the single-step and multi-step discretizations. The implicit dynamics of period-m solutions in discrete nonlinear systems are discussed. The book also offers a generalized approach to finding analytical and numerical solutions of stable and unstable periodic flows to chaos in nonlinear systems with/without time-delay. The bifurcation trees of periodic motions to chaos in the Duffing oscillator are shown as a sample problem, while the discrete Fourier series of periodic motions and chaos are also presented. The book offers a valuable resource for university students, professors, researchers and engineers in the fields of applied mathematics, physics, mechanics, control systems, and engineering.
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