Discretization and Implicit Mapping Dynamics - Luo, Albert C. J.

. .

Résumé :
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.

Biographie:
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 , and he has published over 40 books and more than 350 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, and an associate editor for ASME Journal of Computational and Nonlinear Dynamics. He now serves as Co-editor of the Journal of Applied Nonlinear Dynamics and Editor of various book series, including Nonlinear Systems and Complexity and Nonlinear Physical Science.His major contributions on nonlinear dynamical systems are: ? A theory for stochastic and resonant layers in nonlinear Hamiltonian systems ? A local theory and singularity for discontinuous dynamical systems ? Flow barriers theory for discontinuous dynamical systems ? Synchronization of continuous dynamical systems under specific constraints ? Synchronization and companion of discrete dynamical systems? Analytical solutions of periodic motions in nonlinear systems ? Discretization and implicit mapping dynamics in nonlinear dynamical systems ? Periodic flows in time-delay systems ? Memorized nonlinear dynamical systems In addition, Luo developed accurate theories for nonlinear deformable-body dynamics, machine tool dynamics and others: ? An approximate plate theory ? A theory for soft structures ? A nonlinear theory for beams and rods ? Fluid-induced nonlinear structural vibration ? A large damage theory for anisotropic materials ? A generalized fractal theory He has published over 350 peer-reviewed journal and conference papers. Luo has been an editor for the Journal Communications in Nonlinear Science and Numerical simulation, and the book series on Nonlinear Systems and Complexity (Springer), and Nonlinear Physical Science (Higher Education Press and Springer)....

Sommaire:
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....