03869nam 22007335 450 991030040060332120200707031153.03-662-47275-910.1007/978-3-662-47275-0(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,1867-8440Description 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,1867-8440Statistical physicsDifference equationsFunctional equationsVibrationDynamical systemsDynamicsApplications of Nonlinear Dynamics and Chaos Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/P33020Difference and Functional Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12031Vibration, Dynamical Systems, Controlhttps://scigraph.springernature.com/ontologies/product-market-codes/T15036Statistical physics.Difference equations.Functional equations.Vibration.Dynamical systems.Dynamics.Applications of Nonlinear Dynamics and Chaos Theory.Difference and Functional Equations.Vibration, Dynamical Systems, Control.515.35Luo Albert C. Jauthttp://id.loc.gov/vocabulary/relators/aut720985MiAaPQMiAaPQMiAaPQBOOK9910300400603321Discretization and Implicit Mapping Dynamics1771399UNINA