Albert C. J. Luo

Discretization and Implicit Mapping Dynamics

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Nonlinear Physical Science
• Verlag: Higher Education Press / Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-662-51709-3
• Seitenzahl: 320
• Erscheinungstermin: 23. Oktober 2016
• Englisch
• Abmessung: 235mm x 155mm x 17mm
• Gewicht: 575g
• ISBN-13: 9783662517093
• ISBN-10: 3662517094
• Artikelnr.: 49126784

Autorenporträt

Prof. Yeyin Xu is now an assistant professor at Xi'an Jiaotong University, China. Prof. Jianzhe Huang is now an associate professor at School of Aeronautics and Astronautics, Shanghai Jiao Tong University, China. Prof. Albert C. J. Luo is a distinguished research professor at the Department of Mechanical Engineering at Southern Illinois University Edwardsville, USA. He received his Ph.D. degree from the University of Manitoba, Canada, in 1995. His research focuses on nonlinear dynamics, nonlinear mechanics, and nonlinear differential equations. He has published over 50 monographs, 20 edited books and more than 400 journal articles and conference papers in these fields. He received the Paul Simon Outstanding Scholar Award in 2008 and an ASME fellowship in 2007. He was an editor for Communications in Nonlinear Science and Numerical Simulation for 14 years and an associate editor for ASME Journal of Computational and Nonlinear Dynamics, and International Journal of Bifurcation and Chaos. He now serves as a co-editor of the Journal of Applied Nonlinear Dynamics and editor of various book series, including "Nonlinear Systems and Complexity" and "Nonlinear Physical Science."

Inhaltsangabe

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