Discretization and implicit mapping dynamics [electronic resource] / Albert C.J. Luo.
2015
TA347.D45
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Details
Title
Discretization and implicit mapping dynamics [electronic resource] / Albert C.J. Luo.
Author
Luo, Albert C. J., author.
ISBN
9783662472750 electronic book
3662472759 electronic book
9783662472743
3662472759 electronic book
9783662472743
Published
Heidelberg : Springer ; Beijing : Higher Education Press, 2015.
Language
English
Description
1 online resource : illustrations
Call Number
TA347.D45
Dewey Decimal Classification
515.35
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Series
Nonlinear physical science.
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Table of Contents
Introduction
Nonlinear Discrete Systems
Discretization of Continuous Systems
Implicit Mapping Dynamics
Periodic Flows in Continuous Systems
Periodic Motions to Chaos in Duffing Oscillator.
Nonlinear Discrete Systems
Discretization of Continuous Systems
Implicit Mapping Dynamics
Periodic Flows in Continuous Systems
Periodic Motions to Chaos in Duffing Oscillator.