Understanding Nonlinear Dynamics

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Author: Daniel Kaplan,Leon Glass

Publisher: Springer Science & Business Media

ISBN: 1461208238

Category: Mathematics

Page: 420

View: 1713

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics ( TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. About the Authors Daniel Kaplan specializes in the analysis of data using techniques motivated by nonlinear dynamics. His primary interest is in the interpretation of irregular physiological rhythms, but the methods he has developed have been used in geo physics, economics, marine ecology, and other fields. He joined McGill in 1991, after receiving his Ph.D from Harvard University and working at MIT. His un dergraduate studies were completed at Swarthmore College. He has worked with several instrumentation companies to develop novel types of medical monitors.

Modeling in Biopharmaceutics, Pharmacokinetics and Pharmacodynamics

Homogeneous and Heterogeneous Approaches

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Author: Panos Macheras,Athanassios Iliadis

Publisher: Springer Science & Business Media

ISBN: 0387319107

Category: Mathematics

Page: 444

View: 7502

This book presents a novel modeling approach to biopharamceutics, pharmacokinetics and pharmacodynamic phenomena. It shows how advanced physical and mathematical methods can expand classical models in order to cover heterogeneous drug-biological processes and therapeutic effects in the body. Throughout, many examples are used to illustrate the intrinsic complexity of drug administration related phenomena in the human, justifying the use of advanced modeling methods.

Perspectives of Nonlinear Dynamics:

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Author: E. Atlee Jackson

Publisher: CUP Archive

ISBN: 9780521426329

Category: Mathematics

Page: 520

View: 7104

The dynamics of physical, chemical, biological, or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. This book is a comprehensive introduction to this field, suited to a broad readership, and reflecting a wide range of applications. Some of the concepts considered are: topological equivalence; embeddings; dimensions and fractals; Poincaré maps and map-dynamics; empirical computational sciences vis-á-vis mathematics; Ulam's synergetics; Turing's instability and dissipative structures; chaos; dynamic entropies; Lorenz and Rossler models; predator-prey and replicator models; FPU and KAM phenomena; solitons and nonsolitons; coupled maps and pattern dynamics; cellular automata.

Nonlinear Dynamics

A Two-Way Trip from Physics to Math

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Author: H.G Solari,M.A Natiello,G.B Mindlin

Publisher: CRC Press

ISBN: 9780750303804

Category: Science

Page: 366

View: 7775

Nonlinear Dynamics: A Two-Way Trip from Physics to Math provides readers with the mathematical tools of nonlinear dynamics to tackle problems in all areas of physics. The selection of topics emphasizes bifurcation theory and topological analysis of dynamical systems. The book includes real-life problems and experiments as well as exercises and worked examples to test understanding.

Nonlinear Dynamics

Integrability, Chaos and Patterns

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Author: Muthusamy Lakshmanan,Shanmuganathan Rajaseekar

Publisher: Springer Science & Business Media

ISBN: 3642556884

Category: Mathematics

Page: 620

View: 6950

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.

Chaos and Nonlinear Dynamics

An Introduction for Scientists and Engineers

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Author: Robert C. Hilborn,Amanda and Lisa Cross Professor of Physics Robert Hilborn

Publisher: Oxford University Press on Demand

ISBN: 9780198507239

Category: Mathematics

Page: 650

View: 3716

This is a comprehensive introduction to the exciting scientific field of nonlinear dynamics for students, scientists, and engineers, and requires only minimal prerequisites in physics and mathematics. The book treats all the important areas in the field and provides an extensive and up-to-date bibliography of applications in all fields of science, social science, economics, and even the arts.

Applications of Chaos and Nonlinear Dynamics in Science and Engineering -

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Author: Santo Banerjee,Lamberto Rondoni

Publisher: Springer

ISBN: 3319170376

Category: Science

Page: 304

View: 3939

Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. his fourth volume concentrates on reviewing further relevant contemporary applications of chaotic and nonlinear dynamics as they apply to the various cuttingedge branches of science and engineering. This encompasses, but is not limited to, topics such as synchronization in complex networks and chaotic circuits, time series analysis, ecological and biological patterns, stochastic control theory and vibrations in mechanical systems. Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘recipe book’ full of tried and tested, successful engineering applications.

A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems

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Author: Elbert E. N. Macau

Publisher: Springer

ISBN: 3319785125

Category: Technology & Engineering

Page: 228

View: 926

This book collects recent developments in nonlinear and complex systems. It provides up-to-date theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers symmetry groups, conservation laws, risk reduction management, barriers in Hamiltonian systems, and synchronization and chaotic transient. Illustrating mathematical modeling applications to nonlinear physics and nonlinear engineering, the book is ideal for academic and industrial researchers concerned with machinery and controls, manufacturing, and controls. · Introduces new concepts for understanding and modeling complex systems; · Explains risk reduction management in complex systems; · Examines the symmetry group approach to understanding complex systems; · Illustrates the relation between transient chaos and crises.

Applications of Chaos and Nonlinear Dynamics in Engineering -

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Author: Santo Banerjee,Mala Mitra,Lamberto Rondoni

Publisher: Springer Science & Business Media

ISBN: 3642219225

Category: Technology & Engineering

Page: 350

View: 5415

Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. This volume concentrates on reviewing the most relevant contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. The book covers the theory as applied to robotics, electronic and communication engineering (for example chaos synchronization and cryptography) as well as to civil and mechanical engineering, where its use in damage monitoring and control is explored). Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘recipe book’ full of tried and tested, successful engineering applications

Nonlinear Dynamics and Chaos

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Author: J. M. T. Thompson,Michael Thompson,H. B. Stewart

Publisher: John Wiley & Sons

ISBN: 9780471876458

Category: Mathematics

Page: 437

View: 1587

Nonlinear dynamics and chaos involves the study of apparent random happenings within a system or process. The subject has wide applications within mathematics, engineering, physics and other physical sciences. Since the bestselling first edition was published, there has been a lot of new research conducted in the area of nonlinear dynamics and chaos. * Expands on the bestselling, highly regarded first edition * A new chapter which will cover the new research in the area since first edition * Glossary of terms and a bibliography have been added * All figures and illustrations will be 'modernised' * Comprehensive and systematic account of nonlinear dynamics and chaos, still a fast-growing area of applied mathematics * Highly illustrated * Excellent introductory text, can be used for an advanced undergraduate/graduate course text

Differentialgleichungen und ihre Anwendungen

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Author: Martin Braun

Publisher: Springer-Verlag

ISBN: 3642973418

Category: Mathematics

Page: 596

View: 5940

Dieses richtungsweisende Lehrbuch für die Anwendung der Mathematik in anderen Wissenschaftszweigen gibt eine Einführung in die Theorie der gewöhnlichen Differentialgleichungen. Fortran und APL-Programme geben den Studenten die Möglichkeit, verschiedene numerische Näherungsverfahren an ihrem PC selbst durchzurechnen. Aus den Besprechungen: "Die Darstellung ist überall mathematisch streng und zudem ungemein anregend. Abgesehen von manchen historischen Bemerkungen ... tragen dazu die vielen mit ausführlichem Hintergrund sehr eingehend entwickelten praktischen Anwendungen bei. ... Besondere Aufmerksamkeit wird der physikalisch und technisch so wichtigen Frage nach Stabilität von Lösungen eines Systems von Differentialgleichungen gewidmet. Das Buch ist wegen seiner geringen Voraussetzungen und vorzüglichen Didaktik schon für alle Studenten des 3. Semesters geeignet; seine eminent praktische Haltung empfiehlt es aber auch für alle Physiker, die mit Differentialgleichungen und ihren Anwendungen umzugehen haben." #Physikalische Blätter#

Infinite-Dimensional Dynamical Systems in Mechanics and Physics

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Author: Roger Temam

Publisher: Springer

ISBN: 9780387966380

Category: Mathematics

Page: 500

View: 2321

This is the first attempt at a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics. Other areas of science and technology are included where appropriate. The relation between infinite and finite dimensional systems is presented from a synthetic viewpoint and equations considered include reaction-diffusion, Navier-Stokes and other fluid mechanics equations, magnetohydrodynamics, thermohydraulics, pattern formation, Ginzburg-Landau, damped wave and an introduction to inertial manifolds.

Einführung in die Mechanik und Symmetrie

Eine grundlegende Darstellung klassischer mechanischer Systeme

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Author: Jerrold E. Marsden,Tudor S. Ratiu

Publisher: Springer-Verlag

ISBN: 3642568599

Category: Mathematics

Page: 598

View: 9101

Symmetrie spielt in der Mechanik eine große Rolle. Dieses Buch beschreibt die Entwicklung zugrunde liegender Theorien. Besonderes Gewicht wird der Symmetrie beigemessen. Ursache hierfür sind Entwicklungen im Bereich dynamischer Systeme, der Einsatz geometrischer Verfahren und neue Anwendungen. Dieses Lehrbuch stellt Grundlagen bereit und beschreibt zahlreiche spezifische Anwendungen. Interessant für Physiker und Ingenieure. Ausgewählte Beispiele, Anwendungen, aktuelle Verfahren/Techniken veranschaulichen die Theorie.

Topics in Nonlinear Dynamics with Computer Algebra

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Author: R.H. Rand

Publisher: CRC Press

ISBN: 9782884491136

Category: Mathematics

Page: 229

View: 4792

This text was developed by Dr. Rand over several years of graduate-level instruction in advanced dynamics, nonliner vibrations, and perturbation methods. It presents a variety of topics in nonlinear dynamics, simply explained and modernized through the use of the MACSYMA computer algebra system. The emphasis is on using computer algebra as a tool for the derivation and the solution of nonlinear differential equations and encourages in-depth understanding of the physical and mathematical principles involved. Algebraic principles are presented in conjuction with examples, references, exercises and MACSYMA computer programs.

Nonlinear Dynamics and Stochastic Mechanics

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Author: Wolfgang Kliemann,William F. Langford,Navaratnam Sri Namachchivaya

Publisher: American Mathematical Soc.

ISBN: 0821802577

Category: Technology & Engineering

Page: 238

View: 9502

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. Features: Joins problems in engineering science to recent developments in the mathematical theory of dynamical systems. Offers novel applications of dynamical systems theory. Presents numerical methods for stochastic systems. Compares analytical and numerical studies near the onset of chaos. In one volume, brings together and contrasts deterministic and stochastic models of ``chaos''.

Nonlinear Systems, Vol. 2

Nonlinear Phenomena in Biology, Optics and Condensed Matter

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Author: Juan F. R. Archilla,Faustino Palmero,M. Carmen Lemos,Bernardo Sánchez-Rey,Jesús Casado-Pascual

Publisher: Springer

ISBN: 3319722182

Category: Science

Page: 340

View: 4100

This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction arrays, waveguide arrays, photonic crystals and optical fibers. Nonlinear excitations are inherent to Bose-Einstein Condensates, constituting an excellent benchmark for testing their properties and providing a pathway for future discoveries in fundamental physics.

Nonlinear Dynamics and Time Series

Building a Bridge Between the Natural and Statistical Sciences

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Author: Colleen D. Cutler,Daniel T. Kaplan

Publisher: American Mathematical Soc.

ISBN: 9780821871195

Category: Mathematics

Page: 252

View: 3545

Lars Ahlfors's Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a self-contained treatment of the Beltrami equation, and cover the basic properties of Teichmuller spaces, including the Bers embedding and the Teichmuller curve. It isremarkable how Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmuller spaces from these lecture notes. This editionincludes three new chapters. The first, written by Earle and Kra, describes further developments in the theory of Teichmuller spaces and provides many references to the vast literature on Teichmuller spaces and quasiconformal mappings. The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. The third, by Hubbard, illustrates the role of these mappings in Thurston's theory of hyperbolic structures on 3-manifolds. Together, these threenew chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings. This book is a collection of research and expository papers reflecting the interfacing of two fields: nonlinear dynamics (in the physiological and biological sciences) and statistics. It presents theproceedings of a four-day workshop entitled ''Nonlinear Dynamics and Time Series: Building a Bridge Between the Natural and Statistical Sciences'' held at the Centre de Recherches Mathematiques (CRM) in Montreal in July 1995. The goal of the workshop was to provide an exchange forum and to create a link between two diverse groups with a common interest in the analysis of nonlinear time series data. The editors and peer reviewers of this work have attempted to minimize the problems ofmaintaining communication between the different scientific fields. The result is a collection of interrelated papers that highlight current areas of research in statistics that might have particular applicability to nonlinear dynamics and new methodology and open data analysis problems in nonlinear dynamicsthat might find their way into the toolkits and research interests of statisticians. Features: A survey of state-of-the-art developments in nonlinear dynamics time series analysis with open statistical problems and areas for further research. Contributions by statisticians to understanding and improving modern techniques commonly associated with nonlinear time series analysis, such as surrogate data methods and estimation of local Lyapunov exponents. Starting point for both scientists andstatisticians who want to explore the field. Expositions that are readable to scientists outside the featured fields of specialization. Information for our distributors: Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario,Canada).

Nonlinear Dynamics and Quantum Chaos

An Introduction

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Author: Sandro Wimberger

Publisher: Springer

ISBN: 331906343X

Category: Science

Page: 206

View: 2789

The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.

Philosophy of Complex Systems

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Author: N.A

Publisher: Elsevier

ISBN: 9780080931227

Category: Philosophy

Page: 952

View: 3760

The domain of nonlinear dynamical systems and its mathematical underpinnings has been developing exponentially for a century, the last 35 years seeing an outpouring of new ideas and applications and a concomitant confluence with ideas of complex systems and their applications from irreversible thermodynamics. A few examples are in meteorology, ecological dynamics, and social and economic dynamics. These new ideas have profound implications for our understanding and practice in domains involving complexity, predictability and determinism, equilibrium, control, planning, individuality, responsibility and so on. Our intention is to draw together in this volume, we believe for the first time, a comprehensive picture of the manifold philosophically interesting impacts of recent developments in understanding nonlinear systems and the unique aspects of their complexity. The book will focus specifically on the philosophical concepts, principles, judgments and problems distinctly raised by work in the domain of complex nonlinear dynamical systems, especially in recent years. -Comprehensive coverage of all main theories in the philosophy of Complex Systems -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields are also included