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Nonlinear Dynamics and Stochastic Mechanics

Author: Wolfgang Kliemann

Publisher: CRC Press

Published: 2018-05-04

Total Pages: 302

ISBN-13: 1351091956

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Engineering systems have played a crucial role in stimulating many of the modern developments in nonlinear and stochastic dynamics. After 20 years of rapid progress in these areas, this book provides an overview of the current state of nonlinear modeling and analysis for mechanical and structural systems. This volume is a coherent compendium written by leading experts from the United States, Canada, Western and Eastern Europe, and Australia. The 22 articles describe the background, recent developments, applications, and future directions in bifurcation theory, chaos, perturbation methods, stochastic stability, stochastic flows, random vibrations, reliability, disordered systems, earthquake engineering, and numerics. The book gives readers a sophisticated toolbox that will allow them to tackle modeling problems in mechanical systems that use stochastic and nonlinear dynamics ideas. An extensive bibliography and index ensure this volume will remain a reference standard for years to come.

Book Synopsis Nonlinear Dynamics and Stochastic Mechanics by : Wolfgang Kliemann

Download or read book Nonlinear Dynamics and Stochastic Mechanics written by Wolfgang Kliemann and published by CRC Press. This book was released on 2018-05-04 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineering systems have played a crucial role in stimulating many of the modern developments in nonlinear and stochastic dynamics. After 20 years of rapid progress in these areas, this book provides an overview of the current state of nonlinear modeling and analysis for mechanical and structural systems. This volume is a coherent compendium written by leading experts from the United States, Canada, Western and Eastern Europe, and Australia. The 22 articles describe the background, recent developments, applications, and future directions in bifurcation theory, chaos, perturbation methods, stochastic stability, stochastic flows, random vibrations, reliability, disordered systems, earthquake engineering, and numerics. The book gives readers a sophisticated toolbox that will allow them to tackle modeling problems in mechanical systems that use stochastic and nonlinear dynamics ideas. An extensive bibliography and index ensure this volume will remain a reference standard for years to come.

Nonlinear Dynamics and Stochastic Mechanics

Author: Wolfgang Kliemann

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 250

ISBN-13: 0821802577

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This volume contains the proceedings of the International Symposium on Nonlinear Dynamics and Stochastic Mechanics held at The Fields Institute for Research in Mathematical Sciences from August September (1993) as part of the 1992-1993 Program Year on Dynamical Systems and Bifurcation Theory. In recent years, mathematicians and applied scientists have made significant progress in understanding and have developed powerful tools for the analysis of the complex behavior of deterministic and stochastic dynamical systems. By moving beyond classical perturbation methods to more general geometrical, computational, and analytical methods, this book is at the forefront in transferring these new mathematical ideas into engineering practice. This work presents the solutions of some specific problems in engineering structures and mechanics and demonstrates by explicit example these new methods of solution.

Book Synopsis Nonlinear Dynamics and Stochastic Mechanics by : Wolfgang Kliemann

Download or read book Nonlinear Dynamics and Stochastic Mechanics written by Wolfgang Kliemann and published by American Mathematical Soc.. This book was released on 1996 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the International Symposium on Nonlinear Dynamics and Stochastic Mechanics held at The Fields Institute for Research in Mathematical Sciences from August September (1993) as part of the 1992-1993 Program Year on Dynamical Systems and Bifurcation Theory. In recent years, mathematicians and applied scientists have made significant progress in understanding and have developed powerful tools for the analysis of the complex behavior of deterministic and stochastic dynamical systems. By moving beyond classical perturbation methods to more general geometrical, computational, and analytical methods, this book is at the forefront in transferring these new mathematical ideas into engineering practice. This work presents the solutions of some specific problems in engineering structures and mechanics and demonstrates by explicit example these new methods of solution.

Nonlinear Dynamics and Stochastic Mechanics

Author: Wei-Chau Xie

Publisher:

Published: 2000

Total Pages: 140

ISBN-13:

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Thirteen papers from a November 2000 meeting examine central topics in theory and applications of nonlinear dynamics, stochastic mechanics and dynamics, and control of nonlinear mechanical and structural systems. Papers address topics related to fundamental, applied, analytical, computational, and e

Book Synopsis Nonlinear Dynamics and Stochastic Mechanics by : Wei-Chau Xie

Download or read book Nonlinear Dynamics and Stochastic Mechanics written by Wei-Chau Xie and published by . This book was released on 2000 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thirteen papers from a November 2000 meeting examine central topics in theory and applications of nonlinear dynamics, stochastic mechanics and dynamics, and control of nonlinear mechanical and structural systems. Papers address topics related to fundamental, applied, analytical, computational, and e

Nonlinear Stochastic Systems in Physics and Mechanics

Author: N. Bellomo

Publisher: World Scientific

Published: 1987

Total Pages: 268

ISBN-13: 9789971502492

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This book presents the conceptional line which goes from the observation of physical systems to their modeling and analysis by ordinary differential nonlinear stochastic equations.First, the problems of the mathematical modeling of physical systems are developed. These mathematical models are then classified in terms of ordinary differential stochastic equations from which both qualitative and quantitative results are developed.Each one of the various subjects are methods dealt with ends with an application in mathematical physics or in nonlinear mechanics.

Book Synopsis Nonlinear Stochastic Systems in Physics and Mechanics by : N. Bellomo

Download or read book Nonlinear Stochastic Systems in Physics and Mechanics written by N. Bellomo and published by World Scientific. This book was released on 1987 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the conceptional line which goes from the observation of physical systems to their modeling and analysis by ordinary differential nonlinear stochastic equations.First, the problems of the mathematical modeling of physical systems are developed. These mathematical models are then classified in terms of ordinary differential stochastic equations from which both qualitative and quantitative results are developed.Each one of the various subjects are methods dealt with ends with an application in mathematical physics or in nonlinear mechanics.

Nonlinear Dynamics of Chaotic and Stochastic Systems

Author: Vadim S. Anishchenko

Publisher: Springer Science & Business Media

Published: 2007-07-20

Total Pages: 463

ISBN-13: 3540381686

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We present an improved and enlarged version of our book Nonlinear - namics of Chaotic and Stochastic Systems published by Springer in 2002. Basically, the new edition of the book corresponds to its ?rst version. While preparingthiseditionwemadesomeclari?cationsinseveralsectionsandalso corrected the misprints noticed in some formulas. Besides, three new sections have been added to Chapter 2. They are “Statistical Properties of Dynamical Chaos,” “E?ects of Synchronization in Extended Self-Sustained Oscillatory Systems,” and “Synchronization in Living Systems.” The sections indicated re?ect the most interesting results obtained by the authors after publication of the ?rst edition. We hope that the new edition of the book will be of great interest for a widesectionofreaderswhoarealreadyspecialistsorthosewhoarebeginning research in the ?elds of nonlinear oscillation and wave theory, dynamical chaos, synchronization, and stochastic process theory. Saratov, Berlin, and St. Louis V.S. Anishchenko November 2006 A.B. Neiman T.E. Vadiavasova V.V. Astakhov L. Schimansky-Geier Preface to the First Edition Thisbookisdevotedtotheclassicalbackgroundandtocontemporaryresults on nonlinear dynamics of deterministic and stochastic systems. Considerable attentionisgiventothee?ectsofnoiseonvariousregimesofdynamicsystems with noise-induced order. On the one hand, there exists a rich literature of excellent books on n- linear dynamics and chaos; on the other hand, there are many marvelous monographs and textbooks on the statistical physics of far-from-equilibrium andstochasticprocesses.Thisbookisanattempttocombinetheapproachof nonlinear dynamics based on the deterministic evolution equations with the approach of statistical physics based on stochastic or kinetic equations. One of our main aims is to show the important role of noise in the organization and properties of dynamic regimes of nonlinear dissipative systems.

Book Synopsis Nonlinear Dynamics of Chaotic and Stochastic Systems by : Vadim S. Anishchenko

Download or read book Nonlinear Dynamics of Chaotic and Stochastic Systems written by Vadim S. Anishchenko and published by Springer Science & Business Media. This book was released on 2007-07-20 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present an improved and enlarged version of our book Nonlinear - namics of Chaotic and Stochastic Systems published by Springer in 2002. Basically, the new edition of the book corresponds to its ?rst version. While preparingthiseditionwemadesomeclari?cationsinseveralsectionsandalso corrected the misprints noticed in some formulas. Besides, three new sections have been added to Chapter 2. They are “Statistical Properties of Dynamical Chaos,” “E?ects of Synchronization in Extended Self-Sustained Oscillatory Systems,” and “Synchronization in Living Systems.” The sections indicated re?ect the most interesting results obtained by the authors after publication of the ?rst edition. We hope that the new edition of the book will be of great interest for a widesectionofreaderswhoarealreadyspecialistsorthosewhoarebeginning research in the ?elds of nonlinear oscillation and wave theory, dynamical chaos, synchronization, and stochastic process theory. Saratov, Berlin, and St. Louis V.S. Anishchenko November 2006 A.B. Neiman T.E. Vadiavasova V.V. Astakhov L. Schimansky-Geier Preface to the First Edition Thisbookisdevotedtotheclassicalbackgroundandtocontemporaryresults on nonlinear dynamics of deterministic and stochastic systems. Considerable attentionisgiventothee?ectsofnoiseonvariousregimesofdynamicsystems with noise-induced order. On the one hand, there exists a rich literature of excellent books on n- linear dynamics and chaos; on the other hand, there are many marvelous monographs and textbooks on the statistical physics of far-from-equilibrium andstochasticprocesses.Thisbookisanattempttocombinetheapproachof nonlinear dynamics based on the deterministic evolution equations with the approach of statistical physics based on stochastic or kinetic equations. One of our main aims is to show the important role of noise in the organization and properties of dynamic regimes of nonlinear dissipative systems.

Nonlinear Dynamics and Chaos

Author: Steven H. Strogatz

Publisher: CRC Press

Published: 2018-05-04

Total Pages: 532

ISBN-13: 0429961111

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This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Book Synopsis Nonlinear Dynamics and Chaos by : Steven H. Strogatz

Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Nonlinear Dynamics of Chaotic and Stochastic Systems

Author: Vadim S. Anishchenko

Publisher: Springer Science & Business Media

Published: 2003-01-22

Total Pages: 396

ISBN-13: 9783540424192

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Contains both an exhaustive introduction to the subject as well as a detailed discussion of fundamental problems and research results. Despite the unified presentation of the subject, care has been taken to present the material in largely self-contained chapters.

Book Synopsis Nonlinear Dynamics of Chaotic and Stochastic Systems by : Vadim S. Anishchenko

Nonlinear Stochastic Mechanics

Author: Nicola Bellomo

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 546

ISBN-13: 3642847897

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The Symposium, held in Torino (lSI, Villa Gualino) July 1-5, 1991 is the sixth of a series of IUTAM-Symposia on the application of stochastic analysis to continuum and discrete mechanics. The previous one, held in Innsbruck (1987), was mainly concentrated on qual itative and quantitative analysis of stochastic dynamical systems as well as on bifurcation and transition to chaos of deterministic systems. This Symposium concentrated on fundamental aspects (stochastic analysis and mathe matical methods), on specific applications in various branches of mechanics, engineering and applied sciences as well as on related fields as analysis of large systems, system identifica tion, earthquake prediction. Numerical methods suitable to provide quantitative results, say stochastic finite elements, approximation of probability distribution and direct integration of differential equations have also been the object of interesting presentations. Specific topics of the sessions have been: Engineering Applications, Equivalent Lineariza tion of Discrete Stochastic Systems, Fatigue and Life Estimation, Fluid Dynamics, Numerical Methods, Random Vibration, Reliability Analysis, Stochastic Differential Equations, System Identification, Stochastic Control. We are indebted to the IUTAM Bureau for having promoted and sponsored this Sympo sium and the Scientific Committee for having collaborated to the selection of participants and lecturers as well as to a prompt reviewing of the papers submitted for publication into these proceedings. A special thank is due to Frank Kozin: the organization of this meeting was for him ';ery important; he missed the meeting but his organizer ability was present.

Book Synopsis Nonlinear Stochastic Mechanics by : Nicola Bellomo

Download or read book Nonlinear Stochastic Mechanics written by Nicola Bellomo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Symposium, held in Torino (lSI, Villa Gualino) July 1-5, 1991 is the sixth of a series of IUTAM-Symposia on the application of stochastic analysis to continuum and discrete mechanics. The previous one, held in Innsbruck (1987), was mainly concentrated on qual itative and quantitative analysis of stochastic dynamical systems as well as on bifurcation and transition to chaos of deterministic systems. This Symposium concentrated on fundamental aspects (stochastic analysis and mathe matical methods), on specific applications in various branches of mechanics, engineering and applied sciences as well as on related fields as analysis of large systems, system identifica tion, earthquake prediction. Numerical methods suitable to provide quantitative results, say stochastic finite elements, approximation of probability distribution and direct integration of differential equations have also been the object of interesting presentations. Specific topics of the sessions have been: Engineering Applications, Equivalent Lineariza tion of Discrete Stochastic Systems, Fatigue and Life Estimation, Fluid Dynamics, Numerical Methods, Random Vibration, Reliability Analysis, Stochastic Differential Equations, System Identification, Stochastic Control. We are indebted to the IUTAM Bureau for having promoted and sponsored this Sympo sium and the Scientific Committee for having collaborated to the selection of participants and lecturers as well as to a prompt reviewing of the papers submitted for publication into these proceedings. A special thank is due to Frank Kozin: the organization of this meeting was for him ';ery important; he missed the meeting but his organizer ability was present.

Nonlinear Dynamics, Chaotic and Complex Systems

Author: Eryk Infeld

Publisher: Cambridge University Press

Published: 1997-06-19

Total Pages: 358

ISBN-13: 9780521582018

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The physics and mathematics of nonlinear dynamics, chaotic and complex systems constitute some of the most fascinating developments of late twentieth century science. It turns out that chaotic bahaviour can be understood, and even utilized, to a far greater degree than had been suspected. Surprisingly, universal constants have been discovered. The implications have changed our understanding of important phenomena in physics, biology, chemistry, economics, medicine and numerous other fields of human endeavor. In this book, two dozen scientists and mathematicians who were deeply involved in the "nonlinear revolution" cover most of the basic aspects of the field.

Book Synopsis Nonlinear Dynamics, Chaotic and Complex Systems by : Eryk Infeld

Download or read book Nonlinear Dynamics, Chaotic and Complex Systems written by Eryk Infeld and published by Cambridge University Press. This book was released on 1997-06-19 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: The physics and mathematics of nonlinear dynamics, chaotic and complex systems constitute some of the most fascinating developments of late twentieth century science. It turns out that chaotic bahaviour can be understood, and even utilized, to a far greater degree than had been suspected. Surprisingly, universal constants have been discovered. The implications have changed our understanding of important phenomena in physics, biology, chemistry, economics, medicine and numerous other fields of human endeavor. In this book, two dozen scientists and mathematicians who were deeply involved in the "nonlinear revolution" cover most of the basic aspects of the field.

Advances in Nonlinear Dynamics and Stochastic Processes II

Author: G. Paladin

Publisher:

Published: 1987

Total Pages: 298

ISBN-13:

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Book Synopsis Advances in Nonlinear Dynamics and Stochastic Processes II by : G. Paladin

Download or read book Advances in Nonlinear Dynamics and Stochastic Processes II written by G. Paladin and published by . This book was released on 1987 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: