Discretization and Implicit Mapping Dynamics [electronic resource] / by Albert C. J. Luo.

By: Luo, Albert C. J [author.]Contributor(s): SpringerLink (Online service)Material type: TextTextSeries: Nonlinear Physical Science: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2015Edition: 1st ed. 2015Description: X, 310 p. 46 illus., 26 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783662472750Subject(s): Physics | Difference equations | Functional equations | Statistical physics | Vibration | Dynamical systems | Dynamics | Physics | Nonlinear Dynamics | Difference and Functional Equations | Vibration, Dynamical Systems, ControlAdditional physical formats: Printed edition:: No titleDDC classification: 621 LOC classification: QC174.7-175.36Online resources: Texto completo
Contents:
Introduction -- Nonlinear Discrete Systems -- Discretization of Continuous Systems -- Implicit Mapping Dynamics -- Periodic Flows in Continuous Systems -- Periodic Motions to Chaos in Duffing Oscillator.
In: Springer eBooksSummary: 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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Springer (Colección 2015) Springer (Colección 2015) BIBLIOTECA GENERAL
Física y Astronomía Physics and Astronomy (Browse shelf) Available
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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.

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