Discretization and Implicit Mapping Dynamics

Nonfiction, Science & Nature, Science, Physics, Chaotic Behavior, Mathematics, Mathematical Analysis
Cover of the book Discretization and Implicit Mapping Dynamics by Albert C. J. Luo, Springer Berlin Heidelberg
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Author: Albert C. J. Luo ISBN: 9783662472750
Publisher: Springer Berlin Heidelberg Publication: July 30, 2015
Imprint: Springer Language: English
Author: Albert C. J. Luo
ISBN: 9783662472750
Publisher: Springer Berlin Heidelberg
Publication: July 30, 2015
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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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