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010   $a3-662-47275-9
024 7 $a10.1007/978-3-662-47275-0
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035   $a(EBL)3567972
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035   $a(PQKBTitleCode)TC0001534660
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035   $a(DE-He213)978-3-662-47275-0
035   $a(MiAaPQ)EBC3567972
035   $a(PPN)187690537
035   $a(EXLCZ)993710000000454286
100   $a20150730d2015      u|         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aDiscretization and Implicit Mapping Dynamics /$fby Albert C. J. Luo
205   $a1st ed. 2015.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2015.
215   $a1 online resource (316 p.)
225 1 $aNonlinear Physical Science,$x1867-8440
300   $aDescription based upon print version of record.
311   $a3-662-47274-0 
320   $aIncludes bibliographical references at the end of each chapters and index.
327   $aIntroduction -- Nonlinear Discrete Systems -- Discretization of Continuous Systems -- Implicit Mapping Dynamics -- Periodic Flows in Continuous Systems -- Periodic Motions to Chaos in Duffing Oscillator.
330   $aThis unique book presents the discretization of continuous systems and implicit mapping dynamics of periodic motions to chaos in continuous nonlinear systems. The stability and bifurcation theory of fixed points in discrete nonlinear dynamical systems is reviewed, and the explicit and implicit maps of continuous dynamical systems are developed through the single-step and multi-step discretizations. The implicit dynamics of period-m solutions in discrete nonlinear systems are discussed. The book also offers a generalized approach to finding analytical and numerical solutions of stable and unstable periodic flows to chaos in nonlinear systems with/without time-delay. The bifurcation trees of periodic motions to chaos in the Duffing oscillator are shown as a sample problem, while the discrete Fourier series of periodic motions and chaos are also presented. The book offers a valuable resource for university students, professors, researchers and engineers in the fields of applied mathematics, physics, mechanics, control systems, and engineering.
410  0$aNonlinear Physical Science,$x1867-8440
606   $aStatistical physics
606   $aDifference equations
606   $aFunctional equations
606   $aVibration
606   $aDynamical systems
606   $aDynamics
606   $aApplications of Nonlinear Dynamics and Chaos Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P33020
606   $aDifference and Functional Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12031
606   $aVibration, Dynamical Systems, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/T15036
615  0$aStatistical physics.
615  0$aDifference equations.
615  0$aFunctional equations.
615  0$aVibration.
615  0$aDynamical systems.
615  0$aDynamics.
615 14$aApplications of Nonlinear Dynamics and Chaos Theory.
615 24$aDifference and Functional Equations.
615 24$aVibration, Dynamical Systems, Control.
676   $a515.35
700   $aLuo$b Albert C. J$4aut$4http://id.loc.gov/vocabulary/relators/aut$0720985
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910300400603321
996   $aDiscretization and Implicit Mapping Dynamics$91771399
997   $aUNINA