Nonlinear Dynamical Systems And Carleman Linearization

Author : Krzysztof Kowalski
Publisher : World Scientific
ISBN 13 : 9789810205874
Total Pages : 196 pages
Book Rating : 4.72/5 ( download)

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Download or read book Nonlinear Dynamical Systems and Carleman Linearization written by Krzysztof Kowalski and published by World Scientific. This book was released on 1991 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Carleman linearization has become a new powerful tool in the study of nonlinear dynamical systems. Nevertheless, there is the general lack of familiarity with the Carleman embedding technique among those working in the field of nonlinear models. This book provides a systematic presentation of the Carleman linearization, its generalizations and applications. It also includes a review of existing alternative methods for linearization of nonlinear dynamical systems. There are probably no books covering such a wide spectrum of linearization algorithms. This book also gives a comprehensive introduction to the Kronecker product of matrices, whereas most books deal with it only superficially. The Kronecker product of matrices plays an important role in mathematics and in applications found in theoretical physics.

Author : Muthusamy Lakshmanan
Publisher : Springer Science & Business Media
ISBN 13 : 3642556884
Total Pages : 628 pages
Book Rating : 4.83/5 ( download)

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Download or read book Nonlinear Dynamics written by Muthusamy Lakshmanan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.

Author : Peter A. Cook
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 234 pages
Book Rating : 4.30/5 ( download)

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Download or read book Nonlinear Dynamical Systems written by Peter A. Cook and published by Prentice Hall. This book was released on 1986 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Krzysztof Kowalski
Publisher : World Scientific
ISBN 13 : 9789810217532
Total Pages : 148 pages
Book Rating : 4.36/5 ( download)

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Download or read book Methods of Hilbert Spaces in the Theory of Nonlinear Dynamical Systems written by Krzysztof Kowalski and published by World Scientific. This book was released on 1994 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first monograph on a new powerful method discovered by the author for the study of nonlinear dynamical systems relying on reduction of nonlinear differential equations to the linear abstract Schr”dinger-like equation in Hilbert space. Besides the possibility of unification of many apparently completely different techniques, the ?quantal? Hilbert space formalism introduced enables new original methods to be discovered for solving nonlinear problems arising in investigation of ordinary and partial differential equations as well as difference equations. Applications covered in the book include symmetries and first integrals, linearization transformations, B„cklund transformations, stroboscopic maps, functional equations involving the case of Feigenbaum-Cvitanovic renormalization equations and chaos.

Author : K Kowalski
Publisher : World Scientific
ISBN 13 : 9814502057
Total Pages : 140 pages
Book Rating : 4.54/5 ( download)

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Download or read book Methods of Hilbert Spaces in the Theory of Nonlinear Dynamical Systems written by K Kowalski and published by World Scientific. This book was released on 1994-07-26 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first monograph on a new powerful method discovered by the author for the study of nonlinear dynamical systems relying on reduction of nonlinear differential equations to the linear abstract Schrödinger-like equation in Hilbert space. Besides the possibility of unification of many apparently completely different techniques, the “quantal” Hilbert space formalism introduced enables new original methods to be discovered for solving nonlinear problems arising in investigation of ordinary and partial differential equations as well as difference equations. Applications covered in the book include symmetries and first integrals, linearization transformations, Bäcklund transformations, stroboscopic maps, functional equations involving the case of Feigenbaum-Cvitanovic renormalization equations and chaos. Contents:IntroductionOrdinary Differential Equations:Evolution Equation in Hilbert SpaceOperator Evolution EquationsSymmetries and First IntegralsAlternative Linearization ApproachesPartial Differential Equations:Evolution Equation in Hilbert SpaceOperator Evolution EquationsSymmetries and First IntegralsDifference Equations:Evolution Equation in Hilbert SpaceOperator Evolution EquationsFunctional EquationsApplications:First IntegralsLinearization TransformationsBäcklund TransformationsFeigenbaum-Cvitanovic Renormalization EquationsChaosAppendices:Hilbert SpacesQuantum MechanicsBose Operators and Coherent StatesPosition and Momentum OperatorsFunctional DerivativeBibliographySymbol IndexSubject Index Readership: Researchers in the field of nonlinear dynamical systems and advanced graduate students. keywords:Nonlinear Dynamical Systems;Classical Mechanics;Carleman Linearization;Koopman Approach;Hilbert Space “… a systematic and detailed presentation of the Hilbert space approach to the theory of nonlinear dynamical systems, a far-reaching generalization of the Carleman embedding.” Mathematical Reviews

Author : Visarath In
Publisher : Springer Science & Business Media
ISBN 13 : 3540856323
Total Pages : 464 pages
Book Rating : 4.20/5 ( download)

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Download or read book Applications of Nonlinear Dynamics written by Visarath In and published by Springer Science & Business Media. This book was released on 2009-02-11 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ?eld of applied nonlinear dynamics has attracted scientists and engineers across many different disciplines to develop innovative ideas and methods to study c- plex behavior exhibited by relatively simple systems. Examples include: population dynamics, ?uidization processes, applied optics, stochastic resonance, ?ocking and ?ightformations,lasers,andmechanicalandelectricaloscillators. Acommontheme among these and many other examples is the underlying universal laws of nonl- ear science that govern the behavior, in space and time, of a given system. These laws are universal in the sense that they transcend the model-speci?c features of a system and so they can be readily applied to explain and predict the behavior of a wide ranging phenomena, natural and arti?cial ones. Thus the emphasis in the past decades has been in explaining nonlinear phenomena with signi?cantly less att- tion paid to exploiting the rich behavior of nonlinear systems to design and fabricate new devices that can operate more ef?ciently. Recently, there has been a series of meetings on topics such as Experimental Chaos, Neural Coding, and Stochastic Resonance, which have brought together many researchers in the ?eld of nonlinear dynamics to discuss, mainly, theoretical ideas that may have the potential for further implementation. In contrast, the goal of the 2007 ICAND (International Conference on Applied Nonlinear Dynamics) was focused more sharply on the implementation of theoretical ideas into actual - vices and systems.

Author : Maria Tomas-Rodriguez
Publisher : Springer
ISBN 13 : 1849961018
Total Pages : 303 pages
Book Rating : 4.11/5 ( download)

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Download or read book Linear, Time-varying Approximations to Nonlinear Dynamical Systems written by Maria Tomas-Rodriguez and published by Springer. This book was released on 2010-01-12 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart from other techniques such as those – well-known – based on differential geometry. The authors cover many aspects of nonlinear systems including stability theory, control design and extensions to distributed parameter systems. Many of the classical and modern control design methods which can be applied to linear, time-varying systems can be extended to nonlinear systems by this technique. The implementation of the control is therefore simple and can be done with well-established classical methods. Many aspects of nonlinear systems, such as spectral theory which is important for the generalisation of frequency domain methods, can be approached by this method.

Author : Denis L. Blackmore
Publisher : World Scientific
ISBN 13 : 9814327158
Total Pages : 563 pages
Book Rating : 4.52/5 ( download)

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Download or read book Nonlinear Dynamical Systems of Mathematical Physics written by Denis L. Blackmore and published by World Scientific. This book was released on 2011 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: This distinctive volume presents a clear, rigorous grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to timely leading-edge developments in the field - including some innovations by the authors themselves - that have not appeared in any other book. The exposition begins with an introduction to modern integrable dynamical systems theory, treating such topics as Liouville?Arnold and Mischenko?Fomenko integrability. This sets the stage for such topics as new formulations of the gradient-holonomic algorithm for Lax integrability, novel treatments of classical integration by quadratures, Lie-algebraic characterizations of integrability, and recent results on tensor Poisson structures. Of particular note is the development via spectral reduction of a generalized de Rham?Hodge theory, related to Delsarte-Lions operators, leading to new Chern type classes useful for integrability analysis. Also included are elements of quantum mathematics along with applications to Whitham systems, gauge theories, hadronic string models, and a supplement on fundamental differential-geometric concepts making this volume essentially self-contained. This book is ideal as a reference and guide to new directions in research for advanced students and researchers interested in the modern theory and applications of integrable (especially infinite-dimensional) dynamical systems.

Author : Leslaw Socha
Publisher : Springer
ISBN 13 : 3540729976
Total Pages : 392 pages
Book Rating : 4.76/5 ( download)

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Download or read book Linearization Methods for Stochastic Dynamic Systems written by Leslaw Socha and published by Springer. This book was released on 2007-11-30 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: For most cases of interest, exact solutions to nonlinear equations describing stochastic dynamical systems are not available. This book details the relatively simple and popular linearization techniques available, covering theory as well as application. It examines models with continuous external and parametric excitations, those that cover the majority of known approaches.

Author : Frank Allgower
Publisher : Elsevier
ISBN 13 : 9780080443034
Total Pages : 524 pages
Book Rating : 4.36/5 ( download)

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Download or read book Nonlinear Control Systems 2004 written by Frank Allgower and published by Elsevier. This book was released on 2005-02-02 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: