TY  - BOOK
AU  - Luo,Albert C.J.
ED  - SpringerLink (Online service)
TI  - Discretization and Implicit Mapping Dynamics
T2  - Nonlinear Physical Science,
SN  - 9783662472750
AV  - QC174.7-175.36 
U1  - 621 23
PY  - 2015///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg, Imprint: Springer
KW  - physics
KW  - Difference equations
KW  - Functional equations
KW  - Statistical physics
KW  - Vibration
KW  - Dynamical systems
KW  - Dynamics
KW  - Physics
KW  - Nonlinear Dynamics
KW  - Difference and Functional Equations
KW  - Vibration, Dynamical Systems, Control
N1  - Introduction -- Nonlinear Discrete Systems -- Discretization of Continuous Systems -- Implicit Mapping Dynamics -- Periodic Flows in Continuous Systems -- Periodic Motions to Chaos in Duffing Oscillator
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-662-47275-0
ER  -