Understanding Nonlinear Dynamics

Author: Daniel Kaplan,Leon Glass

Publisher: Springer Science & Business Media

ISBN: 1461208238

Category: Mathematics

Page: 420

View: 3586


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.

Chaos and Nonlinear Dynamics

An Introduction for Scientists and Engineers

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: 4816


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.

Modeling in Biopharmaceutics, Pharmacokinetics and Pharmacodynamics

Homogeneous and Heterogeneous Approaches

Author: Panos Macheras,Athanassios Iliadis

Publisher: Springer Science & Business Media

ISBN: 0387319107

Category: Mathematics

Page: 444

View: 5520


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.

Nonlinear Dynamics

Integrability, Chaos and Patterns

Author: Muthusamy Lakshmanan,Shanmuganathan Rajaseekar

Publisher: Springer Science & Business Media

ISBN: 3642556884

Category: Mathematics

Page: 620

View: 9072


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.

A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems

Author: Elbert E. N. Macau

Publisher: Springer

ISBN: 3319785125

Category: Technology & Engineering

Page: 228

View: 9491


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.

Nonlinear Dynamics

A Two-Way Trip from Physics to Math

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

Publisher: CRC Press

ISBN: 9780750303804

Category: Science

Page: 366

View: 6425


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.

Applications of Chaos and Nonlinear Dynamics in Science and Engineering -

Author: Santo Banerjee,Lamberto Rondoni

Publisher: Springer

ISBN: 3319170376

Category: Science

Page: 304

View: 8783


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.

Nonlinear Dynamics and Stochastic Mechanics

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

Publisher: American Mathematical Soc.

ISBN: 0821802577

Category: Technology & Engineering

Page: 238

View: 9965


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''.

Perspectives of Nonlinear Dynamics:

Author: E. Atlee Jackson

Publisher: CUP Archive

ISBN: 9780521426329

Category: Mathematics

Page: 520

View: 4687


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, Chaotic and Complex Systems

Proceedings of an International Conference Held in Zakopane, Poland, November 7-12 1995, Plenary Invited Lectures

Author: E. Infeld,A. Galkowski

Publisher: Cambridge University Press

ISBN: 9780521582018

Category: Mathematics

Page: 326

View: 9376


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.

Nonlinear Dynamics in Complex Systems

Theory and Applications for the Life-, Neuro- and Natural Sciences

Author: Armin Fuchs

Publisher: Springer Science & Business Media

ISBN: 3642335527

Category: Mathematics

Page: 238

View: 8205


With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex systems are becoming as frequently implemented as traditional statistical analysis. Unfamiliarity with the terminology and rigorous mathematics may discourage many scientists to adopt these methods for their own work, even though such reluctance in most cases is not justified. This book bridges this gap by introducing the procedures and methods used for analyzing nonlinear dynamical systems. In Part I, the concepts of fixed points, phase space, stability and transitions, among others, are discussed in great detail and implemented on the basis of example elementary systems. Part II is devoted to specific, non-trivial applications: coordination of human limb movement (Haken-Kelso-Bunz model), self-organization and pattern formation in complex systems (Synergetics), and models of dynamical properties of neurons (Hodgkin-Huxley, Fitzhugh-Nagumo and Hindmarsh-Rose). Part III may serve as a refresher and companion of some mathematical basics that have been forgotten or were not covered in basic math courses. Finally, the appendix contains an explicit derivation and basic numerical methods together with some programming examples as well as solutions to the exercises provided at the end of certain chapters. Throughout this book all derivations are as detailed and explicit as possible, and everybody with some knowledge of calculus should be able to extract meaningful guidance follow and apply the methods of nonlinear dynamics to their own work. “This book is a masterful treatment, one might even say a gift, to the interdisciplinary scientist of the future.” “With the authoritative voice of a genuine practitioner, Fuchs is a master teacher of how to handle complex dynamical systems.” “What I find beautiful in this book is its clarity, the clear definition of terms, every step explained simply and systematically.” (J.A.Scott Kelso, excerpts from the foreword)

Applications of Chaos and Nonlinear Dynamics in Engineering -

Author: Santo Banerjee,Mala Mitra,Lamberto Rondoni

Publisher: Springer Science & Business Media

ISBN: 3642219225

Category: Technology & Engineering

Page: 350

View: 7603


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 Time Series

Building a Bridge Between the Natural and Statistical Sciences

Author: Colleen D. Cutler,Daniel T. Kaplan

Publisher: American Mathematical Soc.

ISBN: 0821841858

Category: Mathematics

Page: 252

View: 461


An important interdisciplinary work ... provides a valuable collection of recent research ... should appeal to scientists and statisticians who are relatively new to the field and to others interested in a very readable exploration of the topics covered. --Journal of Computational Intelligence in Finance 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 the proceedings 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.

Nonlinear Dynamics and Chaos

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

Publisher: John Wiley & Sons

ISBN: 9780471876458

Category: Mathematics

Page: 437

View: 7677


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

Nonlinear Dynamics in the Life and Social Sciences

Author: William H. Sulis,Irina Nikolaevna Trofimova

Publisher: IOS Press

ISBN: 9781586030209

Category: Mathematics

Page: 417

View: 9522


Incorporating chaos theory into psychology and the life sciences, this text includes empirical studies of neural encoding, memory, eye movements, warfare, business cycles and selection of time series analysis algorithms. There are theoretical chapters on emergence and social dynamics, and clinical contributions dealing with: the measurement of quality of life for psychiatric patients; psychosis; the organization of self; and the role of love in family dynamics. Finally ideas from non-linear dynamics are applied to understanding the creative process.

Differentialgleichungen und ihre Anwendungen

Author: Martin Braun

Publisher: Springer-Verlag

ISBN: 3642975151

Category: Mathematics

Page: 598

View: 5780


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#

Nonlinear Dynamics and Quantum Chaos

An Introduction

Author: Sandro Wimberger

Publisher: Springer

ISBN: 331906343X

Category: Science

Page: 206

View: 4274


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.

Nonlinear Dynamics in Optical Complex Systems

Author: Kenju Otsuka

Publisher: Springer Science & Business Media

ISBN: 9780792361329

Category: Technology & Engineering

Page: 296

View: 7254


This book is the first comprehensive volume on nonlinear dynamics and chaos in optical systems. A few books have been published recently, but they summarize applied mathematical methodologies toward understanding of nonlinear dynamics in laser systems with small degrees of freedom focusing on linearized perturbation and bifurcation analyses. In contrast to these publications, this book summarizes nonlinear dynamic problems in optical complex systems possessing large degrees of freedom, systematically featuring our original experimental results and their theoretical treatments. The new concepts introduced in this book will have a wide appeal to audiences involved in a rapidly-growing field of nonlinear dynamics. This book focuses on nonlinear dynamics and cooperative functions in realistic optical complex systems, such as multimode lasers, laser array, coupled nonlinear-element systems, and their applications to optical processing. This book is prepared for graduate students majoring in optical and laser physics, but the generic nature of complex systems described in this book may stimulate researchers in the field of nonlinear dynamics covering different academic areas including applied mathematics, hydrodynamics, celestial mechanics, chemistry, biology, and economics.

An Introduction to Complex Systems

Society, Ecology, and Nonlinear Dynamics

Author: Paul Fieguth

Publisher: Springer

ISBN: 3319446061

Category: Science

Page: 346

View: 1213


This undergraduate text explores a variety of large-scale phenomena - global warming, ice ages, water, poverty - and uses these case studies as a motivation to explore nonlinear dynamics, power-law statistics, and complex systems. Although the detailed mathematical descriptions of these topics can be challenging, the consequences of a system being nonlinear, power-law, or complex are in fact quite accessible. This book blends a tutorial approach to the mathematical aspects of complex systems together with a complementary narrative on the global/ecological/societal implications of such systems. Nearly all engineering undergraduate courses focus on mathematics and systems which are small scale, linear, and Gaussian. Unfortunately there is not a single large-scale ecological or social phenomenon that is scalar, linear, and Gaussian. This book offers students insights to better understand the large-scale problems facing the world and to realize that these cannot be solved by a single, narrow academic field or perspective. Instead, the book seeks to emphasize understanding, concepts, and ideas, in a way that is mathematically rigorous, so that the concepts do not feel vague, but not so technical that the mathematics get in the way. The book is intended for undergraduate students in a technical domain such as engineering, computer science, physics, mathematics, and environmental studies.