03597nam 22007335 450 991030040060332120251113204145.03-662-47275-910.1007/978-3-662-47275-0(CKB)3710000000454286(EBL)3567972(SSID)ssj0001534660(PQKBManifestationID)11891369(PQKBTitleCode)TC0001534660(PQKBWorkID)11496485(PQKB)11067010(DE-He213)978-3-662-47275-0(MiAaPQ)EBC3567972(PPN)187690537(EXLCZ)99371000000045428620150730d2015 u| 0engur|n|---|||||txtccrDiscretization and Implicit Mapping Dynamics /by Albert C. J. Luo1st ed. 2015.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2015.1 online resource (316 p.)Nonlinear Physical Science,1867-8459Description based upon print version of record.3-662-47274-0 Includes bibliographical references at the end of each chapters and index.Introduction -- Nonlinear Discrete Systems -- Discretization of Continuous Systems -- Implicit Mapping Dynamics -- Periodic Flows in Continuous Systems -- Periodic Motions to Chaos in Duffing Oscillator.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.Nonlinear Physical Science,1867-8459Nonlinear opticsDifference equationsFunctional equationsMultibody systemsVibrationMechanics, AppliedNonlinear OpticsDifference and Functional EquationsMultibody Systems and Mechanical VibrationsNonlinear optics.Difference equations.Functional equations.Multibody systems.Vibration.Mechanics, Applied.Nonlinear Optics.Difference and Functional Equations.Multibody Systems and Mechanical Vibrations.515.35Luo Albert C. Jauthttp://id.loc.gov/vocabulary/relators/aut720985MiAaPQMiAaPQMiAaPQBOOK9910300400603321Discretization and Implicit Mapping Dynamics1771399UNINA