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Discretization and Implicit Mapping Dynamics

Albert C. J. Luo (Autor)

Buch | Hardcover

X, 310 Seiten

2015 | 1st ed. 2015
Springer Berlin (Verlag)
978-3-662-47274-3 (ISBN)

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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.

Albert C.J. Luo is an internationally recognized professor in nonlinear dynamics and mechanics. He is a Distinguished Research Professor at Southern Illinois University Edwardsville, USA. His principal research interests lie in the fields of Hamiltonian chaos, nonlinear deformable-body dynamics, discontinuous dynamical systems, regularity and complexity in nonlinear systems, analytical and numerical solutions of differential equations.

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

Erscheint lt. Verlag	13.8.2015
Reihe/Serie	Nonlinear Physical Science
Zusatzinfo	X, 310 p. 46 illus., 26 illus. in color.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Optik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
	Technik ► Maschinenbau
Schlagworte	Chaos Duffing Oscillator • Discretization Continuous Systems • Discretization-Implicit Mapping Dynamics- • Implicit Mapping Dynamics • Nonlinear discrete systems • Periodic Flows and Chaos-Bifurcation Trees • to Chaos-Discrete Fourier Series
ISBN-10	3-662-47274-0 / 3662472740
ISBN-13	978-3-662-47274-3 / 9783662472743
Zustand	Neuware