Numerical Continuation Methods For Slow Fast Dynamical Systems
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Numerical Continuation Methods For Slow Fast Dynamical Systems
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Author :
language : en
Publisher:
Release Date : 2009
Numerical Continuation Methods For Slow Fast Dynamical Systems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Numerical Continuation Methods For Dynamical Systems
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Author : Bernd Krauskopf
language : en
Publisher: Springer
Release Date : 2007-11-06
Numerical Continuation Methods For Dynamical Systems written by Bernd Krauskopf and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-06 with Science categories.
Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.
Mathematics Of Complexity And Dynamical Systems
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Author : Robert A. Meyers
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-05
Mathematics Of Complexity And Dynamical Systems written by Robert A. Meyers and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-05 with Mathematics categories.
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Numerical Continuation Methods For Dynamical Systems
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Author : Bernd Krauskopf
language : en
Publisher: Springer
Release Date : 2007-07-26
Numerical Continuation Methods For Dynamical Systems written by Bernd Krauskopf and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-26 with Science categories.
Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.
Multiple Time Scale Dynamics
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Author : Christian Kuehn
language : en
Publisher: Springer
Release Date : 2015-02-25
Multiple Time Scale Dynamics written by Christian Kuehn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-25 with Mathematics categories.
This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.
Topology Based Methods In Visualization Ii
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Author : Hans-Christian Hege
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-07
Topology Based Methods In Visualization Ii written by Hans-Christian Hege and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-07 with Mathematics categories.
Visualization research aims to provide insight into large, complicated data sets and the phenomena behind them. While there are di?erent methods of reaching this goal, topological methods stand out for their solid mathem- ical foundation, which guides the algorithmic analysis and its presentation. Topology-based methods in visualization have been around since the beg- ning of visualization as a scienti?c discipline, but they initially played only a minor role. In recent years,interest in topology-basedvisualization has grown andsigni?cantinnovationhasledto newconceptsandsuccessfulapplications. The latest trends adapt basic topological concepts to precisely express user interests in topological properties of the data. This book is the outcome of the second workshop on Topological Methods in Visualization, which was held March 4–6, 2007 in Kloster Nimbschen near Leipzig,Germany.Theworkshopbroughttogethermorethan40international researchers to present and discuss the state of the art and new trends in the ?eld of topology-based visualization. Two inspiring invited talks by George Haller, MIT, and Nelson Max, LLNL, were accompanied by 14 presentations by participants and two panel discussions on current and future trends in visualization research. This book contains thirteen research papers that have been peer-reviewed in a two-stage review process. In the ?rst phase, submitted papers where peer-reviewed by the international program committee. After the workshop accepted papers went through a revision and a second review process taking into account comments from the ?rst round and discussions at the workshop. Abouthalfthepapersconcerntopology-basedanalysisandvisualizationof ?uid?owsimulations;twopapersconcernmoregeneraltopologicalalgorithms, while theremaining papers discuss topology-based visualization methods in application areas like biology, medical imaging and electromagnetism.
Vibrations And Stability
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Author : Jon Juel Thomsen
language : en
Publisher: Springer Nature
Release Date : 2021-03-18
Vibrations And Stability written by Jon Juel Thomsen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-18 with Technology & Engineering categories.
An ideal text for students that ties together classical and modern topics of advanced vibration analysis in an interesting and lucid manner. It provides students with a background in elementary vibrations with the tools necessary for understanding and analyzing more complex dynamical phenomena that can be encountered in engineering and scientific practice. It progresses steadily from linear vibration theory over various levels of nonlinearity to bifurcation analysis, global dynamics and chaotic vibrations. It trains the student to analyze simple models, recognize nonlinear phenomena and work with advanced tools such as perturbation analysis and bifurcation analysis. Explaining theory in terms of relevant examples from real systems, this book is user-friendly and meets the increasing interest in non-linear dynamics in mechanical/structural engineering and applied mathematics and physics. This edition includes a new chapter on the useful effects of fast vibrations and many new exercise problems.
Topics In Multiple Time Scale Dynamics
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Author : Maximilian Engel
language : en
Publisher: American Mathematical Society
Release Date : 2024-10-21
Topics In Multiple Time Scale Dynamics written by Maximilian Engel and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-21 with Mathematics categories.
This volume contains the proceedings of the BIRS Workshop "Topics in Multiple Time Scale Dynamics," held from November 27? December 2, 2022, at the Banff International Research Station, Banff, Alberta, Canada. The area of multiple-scale dynamics is rapidly evolving, marked by significant theoretical breakthroughs and practical applications. The workshop facilitated a convergence of experts from various sub-disciplines, encompassing topics like blow-up techniques for ordinary differential equations (ODEs), singular perturbation theory for stochastic differential equations (SDE), homogenization and averaging, slow-fast maps, numerical approaches, and network dynamics, including their applications in neuroscience and climate science. This volume provides a wide-ranging perspective on the current challenging subjects being explored in the field, including themes such as novel approaches to blowing-up and canard theory in unique contexts, complex multi-scale challenges in PDEs, and the role of stochasticity in multiple-scale systems.
Applications Of Differential Equations
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Author : Jayant Ramaswamy
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Applications Of Differential Equations written by Jayant Ramaswamy and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
Unlock the power of mathematics with "Applications of Differential Equations," a comprehensive guide that demystifies this essential tool. Our book is crafted for students, educators, and practitioners, offering a deep dive into the theory, techniques, and real-world applications of differential equations across diverse fields, including physics, engineering, biology, and economics. We start with a solid foundation in the basic concepts, making the book accessible to beginners while providing valuable insights for advanced learners. Clear explanations and illustrative examples guide readers through the classification of differential equations, methods for solving first-order equations, and techniques for analyzing their behavior. Step-by-step solutions and practical exercises reinforce learning, ensuring confidence in tackling a wide range of problems. Delving into advanced topics, we cover higher-order differential equations, systems of differential equations, and Laplace transforms. We emphasize mathematical modeling, showcasing how differential equations represent real-world phenomena and predict their behavior. What sets this book apart is its focus on practical applications. Real-world examples and case studies illustrate how differential equations model and analyze phenomena such as population dynamics, fluid mechanics, and electrical circuits. This approach bridges theory and practice, highlighting the versatility and power of differential equations in addressing challenges and advancing knowledge. Designed for a global audience, our book ensures accessibility and relevance for readers from diverse backgrounds. Whether you're a student, educator, or practitioner, "Applications of Differential Equations" is your go-to resource for mastering this powerful mathematical tool.
Singular Perturbations
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Author : Elena Shchepakina
language : en
Publisher: Springer
Release Date : 2014-10-06
Singular Perturbations written by Elena Shchepakina and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-06 with Mathematics categories.
These lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques. It gives many examples and step-by-step techniques, which will help beginners move to a more advanced level. Singularly perturbed systems appear naturally in the modelling of many processes that are characterized by slow and fast motions simultaneously, for example, in fluid dynamics and nonlinear mechanics. This book’s approach consists in separating out the slow motions of the system under investigation. The result is a reduced differential system of lesser order. However, it inherits the essential elements of the qualitative behaviour of the original system. Singular Perturbations differs from other literature on the subject due to its methods and wide range of applications. It is a valuable reference for specialists in the areas of applied mathematics, engineering, physics, biology, as well as advanced undergraduates for the earlier parts of the book, and graduate students for the later chapters.