Regularity And Stochasticity Of Nonlinear Dynamical Systems

Author : Dimitri Volchenkov,Xavier Leoncini
Publisher : Springer
Page : 311 pages
File Size : 40,5 Mb
Release : 2017-06-24
Category : Technology & Engineering
ISBN : 9783319580623

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Regularity and Stochasticity of Nonlinear Dynamical Systems by Dimitri Volchenkov,Xavier Leoncini Pdf

This book presents recent developments in nonlinear dynamics and physics with an emphasis on complex systems. The contributors provide recent theoretic developments and new techniques to solve nonlinear dynamical systems and help readers understand complexity, stochasticity, and regularity in nonlinear dynamical systems. This book covers integro-differential equation solvability, Poincare recurrences in ergodic systems, orientable horseshoe structure, analytical routes of periodic motions to chaos, grazing on impulsive differential equations, from chaos to order in coupled oscillators, and differential-invariant solutions for automorphic systems, inequality under uncertainty.

Author : Albert C. J. Luo
Publisher : Springer Science & Business Media
Page : 500 pages
File Size : 44,7 Mb
Release : 2013-07-12
Category : Mathematics
ISBN : 9781461415237

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Regularity and Complexity in Dynamical Systems by Albert C. J. Luo Pdf

Regularity and Complexity in Dynamical Systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive, discontinuous, and switching systems. In traditional analysis, the periodic and chaotic behaviors in continuous, nonlinear dynamical systems were extensively discussed even if unsolved. In recent years, there has been an increasing amount of interest in periodic and chaotic behaviors in discontinuous dynamical systems because such dynamical systems are prevalent in engineering. Usually, the smoothening of discontinuous dynamical system is adopted in order to use the theory of continuous dynamical systems. However, such technique cannot provide suitable results in such discontinuous systems. In this book, an alternative way is presented to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.

Author : Wolfgang Kliemann,William F. Langford,Navaratnam Sri Namachchivaya
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 55,5 Mb
Release : 1996
Category : Technology & Engineering
ISBN : 9780821802571

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Nonlinear Dynamics and Stochastic Mechanics by Wolfgang Kliemann,William F. Langford,Navaratnam Sri Namachchivaya Pdf

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.

Author : Vadim S. Anishchenko,Vladimir Astakhov,Alexander Neiman,Tatjana Vadivasova,Lutz Schimansky-Geier
Publisher : Springer Science & Business Media
Page : 463 pages
File Size : 47,6 Mb
Release : 2007-07-20
Category : Science
ISBN : 9783540381686

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Nonlinear Dynamics of Chaotic and Stochastic Systems by Vadim S. Anishchenko,Vladimir Astakhov,Alexander Neiman,Tatjana Vadivasova,Lutz Schimansky-Geier Pdf

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.

Author : Dimitri Volchenkov
Publisher : Springer Nature
Page : 198 pages
File Size : 49,5 Mb
Release : 2020-12-14
Category : Mathematics
ISBN : 9789811590344

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Nonlinear Dynamics, Chaos, and Complexity by Dimitri Volchenkov Pdf

This book demonstrates how mathematical methods and techniques can be used in synergy and create a new way of looking at complex systems. It becomes clear nowadays that the standard (graph-based) network approach, in which observable events and transportation hubs are represented by nodes and relations between them are represented by edges, fails to describe the important properties of complex systems, capture the dependence between their scales, and anticipate their future developments. Therefore, authors in this book discuss the new generalized theories capable to describe a complex nexus of dependences in multi-level complex systems and to effectively engineer their important functions. The collection of works devoted to the memory of Professor Valentin Afraimovich introduces new concepts, methods, and applications in nonlinear dynamical systems covering physical problems and mathematical modelling relevant to molecular biology, genetics, neurosciences, artificial intelligence as well as classic problems in physics, machine learning, brain and urban dynamics. The book can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists, urban planners, and even musicians (with some mathematical background).

Author : Wolfgang Kliemann
Publisher : CRC Press
Page : 560 pages
File Size : 41,8 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351083508

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Nonlinear Dynamics and Stochastic Mechanics by Wolfgang Kliemann Pdf

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.

Author : Karl M. Newell,Peter C.M. Molenaar
Publisher : Psychology Press
Page : 365 pages
File Size : 54,8 Mb
Release : 2014-03-05
Category : Psychology
ISBN : 9781317779117

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Applications of Nonlinear Dynamics To Developmental Process Modeling by Karl M. Newell,Peter C.M. Molenaar Pdf

There has been an increasing interest in the application of dynamical systems to the study of development over the last decade. The explosion of the dynamical systems framework in the physical and biological sciences has opened the door to a new Zeitgeist for studying development. This appeal to dynamical systems by developmentalists is natural given the intuitive links between the established fundamental problems of development and the conceptual and operational scope of nonlinear dynamical systems. This promise of a new approach and framework within which to study development has led to some progress in recent years but also a growing appreciation of the difficulty of both fully examining the new metaphor and realizing its potential. Divided into 4 parts, this book is a result of a recent conference on dynamical systems and development held at Pennsylvania State University. The first 3 parts focus on the content domains of development that have given most theoretical and empirical attention to the potential applications of dynamical systems--physical growth and movement, cognition, and communication. These parts show that a range of nonlinear models have been applied to a host of developmental phenomena. Part 4 highlights two particular methodological issues that hold important implications for the modeling of developmental phenomena with dynamical systems techniques.

Author : Vadim S. Anishchenko,Vladimir Astakhov,Alexander Neiman,Tatjana Vadivasova,Lutz Schimansky-Geier
Publisher : Springer Science & Business Media
Page : 396 pages
File Size : 42,7 Mb
Release : 2003-01-22
Category : Science
ISBN : 3540424199

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Nonlinear Dynamics of Chaotic and Stochastic Systems by Vadim S. Anishchenko,Vladimir Astakhov,Alexander Neiman,Tatjana Vadivasova,Lutz Schimansky-Geier Pdf

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.

Author : Carla M.A. Pinto
Publisher : Springer Nature
Page : 496 pages
File Size : 55,5 Mb
Release : 2022-10-21
Category : Technology & Engineering
ISBN : 9783031066320

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Nonlinear Dynamics and Complexity by Carla M.A. Pinto Pdf

This book collects a range of contributions on nonlinear dynamics and complexity, providing a systematic summary of recent developments, applications, and overall advances in nonlinearity, chaos, and complexity. It presents both theories and techniques in nonlinear systems and complexity and serves as a basis for more research on synchronization and complexity in nonlinear science as well as a mechanism to fast-scatter the new knowledge to scientists, engineers, and students in the corresponding fields. Written by world-renown experts from across the globe, the collection is ideal for researchers, practicing engineers, and students concerned with machinery and controls, manufacturing, and controls.

Author : Ludwig Arnold
Publisher : Springer Science & Business Media
Page : 590 pages
File Size : 53,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662128787

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Random Dynamical Systems by Ludwig Arnold Pdf

The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.

Author : G. Paladin,A. Vulpiani
Publisher : Unknown
Page : 298 pages
File Size : 46,6 Mb
Release : 1987
Category : Mathematics
ISBN : UCAL:B5162822

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Advances in Nonlinear Dynamics and Stochastic Processes II by G. Paladin,A. Vulpiani Pdf

Author : Steven H. Strogatz
Publisher : CRC Press
Page : 532 pages
File Size : 42,8 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9780429961113

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Nonlinear Dynamics and Chaos by Steven H. Strogatz Pdf

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.

Author : A.J. Lichtenberg,M.A. Lieberman
Publisher : Springer Science & Business Media
Page : 708 pages
File Size : 53,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475721843

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Regular and Chaotic Dynamics by A.J. Lichtenberg,M.A. Lieberman Pdf

This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects.

Author : Daniel Benest,Claude Froeschle
Publisher : Atlantica Séguier Frontières
Page : 662 pages
File Size : 51,9 Mb
Release : 1992
Category : Asteroids
ISBN : 2863321129

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Interrelations Between Physics and Dynamics for Minor Bodies in the Solar System by Daniel Benest,Claude Froeschle Pdf

Author : Boling Guo,Hongjun Gao,Xueke Pu
Publisher : Walter de Gruyter GmbH & Co KG
Page : 228 pages
File Size : 55,8 Mb
Release : 2016-11-21
Category : Mathematics
ISBN : 9783110492439

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Stochastic PDEs and Dynamics by Boling Guo,Hongjun Gao,Xueke Pu Pdf

This book explains mathematical theories of a collection of stochastic partial differential equations and their dynamical behaviors. Based on probability and stochastic process, the authors discuss stochastic integrals, Ito formula and Ornstein-Uhlenbeck processes, and introduce theoretical framework for random attractors. With rigorous mathematical deduction, the book is an essential reference to mathematicians and physicists in nonlinear science. Contents: Preliminaries The stochastic integral and Itô formula OU processes and SDEs Random attractors Applications Bibliography Index