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Nonlinear Physical Science

Discretization and Implicit Mapping Dynamics

Authors: Luo, Albert C. J.

  • The first monograph to discuss the implicit mapping dynamics of periodic flows to chaos
  • Provides both explicit and implicit discrete maps of continuous systems
  • Discusses the implicit dynamics of period-m solutions in discrete nonlinear systems
  • Offers a way to find periodic flows to chaos in nonlinear systems with and without time-delay
  • Presents the discrete Fourier series of discrete nodes of periodic motion
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eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-662-47275-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA in USD
  • ISBN 978-3-662-47274-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.99
price for USA in USD
  • ISBN 978-3-662-51709-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

About the authors

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.

Table of contents (6 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-662-47275-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA in USD
  • ISBN 978-3-662-47274-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.99
price for USA in USD
  • ISBN 978-3-662-51709-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Discretization and Implicit Mapping Dynamics
Authors
Series Title
Nonlinear Physical Science
Copyright
2015
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg
Distribution Rights
Distribution rights in China: Higher Education Press, Beijing, China
eBook ISBN
978-3-662-47275-0
DOI
10.1007/978-3-662-47275-0
Hardcover ISBN
978-3-662-47274-3
Softcover ISBN
978-3-662-51709-3
Series ISSN
1867-8440
Edition Number
1
Number of Pages
X, 310
Number of Illustrations and Tables
20 b/w illustrations, 26 illustrations in colour
Additional Information
Jointly published with Higher Education Press, Beijing, China
Topics