Qualitative Dynamics and Chaos

Qualitative Dynamics and Chaos PDF Author: Arnaldo Rodriguez-Gonzalez
Publisher: Arnaldo Rodriguez-Gonzalez
ISBN:
Category : Mathematics
Languages : en
Pages : 493

Get Book Here

Book Description
This largely self-contained textbook on qualitative dynamics and chaos is intended for a broad audience of readers who are interested in describing systems that change over time using a mathematically simple, but conceptually rigorous, framework centered around descriptive sequences of symbols. This framework also allows readers who may not have a large amount of mathematical training to develop an unambiguous understanding of the notion of chaos and related aspects of dynamical systems theory. Concepts and techniques are introduced in the first parts of the book, which are later expanded to more mathematically abstract ideas in the latter parts of the book. For those who are already have some mathematical training, this text is intended to be an alternative to standard symbolic dynamics textbooks which both mildly generalizes their scope and specifically centers its discussion around dynamical systems theory aspects. It uses the notion of a "falsifiable system"—a type of set of infinite symbol sequences, which is an extension of both formal languages and symbolic dynamical systems—as a central conceptual link between the theory of formal languages and the study of chaos, and allows readers a method to identify chaos within such systems (and systems equivalent to them) by entirely graphical methods. The latter parts of the book then focus on how to apply these methods to understand the dynamics of more traditional, numerically-based systems.

Qualitative Dynamics and Chaos

Qualitative Dynamics and Chaos PDF Author: Arnaldo Rodriguez-Gonzalez
Publisher: Arnaldo Rodriguez-Gonzalez
ISBN:
Category : Mathematics
Languages : en
Pages : 493

Get Book Here

Book Description
This largely self-contained textbook on qualitative dynamics and chaos is intended for a broad audience of readers who are interested in describing systems that change over time using a mathematically simple, but conceptually rigorous, framework centered around descriptive sequences of symbols. This framework also allows readers who may not have a large amount of mathematical training to develop an unambiguous understanding of the notion of chaos and related aspects of dynamical systems theory. Concepts and techniques are introduced in the first parts of the book, which are later expanded to more mathematically abstract ideas in the latter parts of the book. For those who are already have some mathematical training, this text is intended to be an alternative to standard symbolic dynamics textbooks which both mildly generalizes their scope and specifically centers its discussion around dynamical systems theory aspects. It uses the notion of a "falsifiable system"—a type of set of infinite symbol sequences, which is an extension of both formal languages and symbolic dynamical systems—as a central conceptual link between the theory of formal languages and the study of chaos, and allows readers a method to identify chaos within such systems (and systems equivalent to them) by entirely graphical methods. The latter parts of the book then focus on how to apply these methods to understand the dynamics of more traditional, numerically-based systems.

Methods Of Qualitative Theory In Nonlinear Dynamics (Part I)

Methods Of Qualitative Theory In Nonlinear Dynamics (Part I) PDF Author: Leonid P Shilnikov
Publisher: World Scientific
ISBN: 9814496421
Category : Science
Languages : en
Pages : 418

Get Book Here

Book Description
Bifurcation and Chaos has dominated research in nonlinear dynamics for over two decades and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book is written to serve the above unfulfilled need.Following the footsteps of Poincaré, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in this book were developed only recently and have not yet appeared in a textbook form.In keeping with the self-contained nature of this book, all topics are developed with an introductory background and complete mathematical rigor. Generously illustrated and written with a high level of exposition, this book will appeal to both beginners and advanced students of nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.

Nonlinear Dynamics and Chaos

Nonlinear Dynamics and Chaos PDF Author: Steven H. Strogatz
Publisher: CRC Press
ISBN: 0429961111
Category : Mathematics
Languages : en
Pages : 532

Get Book Here

Book Description
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.

Complex and Chaotic Nonlinear Dynamics

Complex and Chaotic Nonlinear Dynamics PDF Author: Thierry Vialar
Publisher: Springer Science & Business Media
ISBN: 3540859780
Category : Business & Economics
Languages : en
Pages : 752

Get Book Here

Book Description
Complex dynamics constitute a growing and increasingly important area as they offer a strong potential to explain and formalize natural, physical, financial and economic phenomena. This book pursues the ambitious goal to bring together an extensive body of knowledge regarding complex dynamics from various academic disciplines. Beyond its focus on economics and finance, including for instance the evolution of macroeconomic growth models towards nonlinear structures as well as signal processing applications to stock markets, fundamental parts of the book are devoted to the use of nonlinear dynamics in mathematics, statistics, signal theory and processing. Numerous examples and applications, almost 700 illustrations and numerical simulations based on the use of Matlab make the book an essential reference for researchers and students from many different disciplines who are interested in the nonlinear field. An appendix recapitulates the basic mathematical concepts required to use the book.

Methods of Qualitative Theory in Nonlinear Dynamics

Methods of Qualitative Theory in Nonlinear Dynamics PDF Author: L. P. Shil'nikov
Publisher: World Scientific
ISBN: 9812798552
Category : Mathematics
Languages : en
Pages : 591

Get Book Here

Book Description
Bifurcation and chaos has dominated research in nonlinear dynamics for over two decades, and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book has been written to serve that unfulfilled need. Following the footsteps of Poincar(r), and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in the book have been developed only recently and have not yet appeared in textbook form. In keeping with the self-contained nature of the book, all the topics are developed with introductory background and complete mathematical rigor. Generously illustrated and written at a high level of exposition, this invaluable book will appeal to both the beginner and the advanced student of nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject. Sample Chapter(s). Introduction to Part II (124 KB). Chapter 7.1: Rough systems on a plane. Andronov-Pontryagin theorem (218 KB). Chapter 7.2: The set of center motions (158 KB). Chapter 7.3: General classification of center motions (155 KB). Chapter 7.4: Remarks on roughness of high-order dynamical systems (136 KB). Chapter 7.5: Morse-Smale systems (435 KB). Chapter 7.6: Some properties of Morse-Smale systems (211 KB). Contents: Structurally Stable Systems; Bifurcations of Dynamical Systems; The Behavior of Dynamical Systems on Stability Boundaries of Equilibrium States; The Behavior of Dynamical Systems on Stability Boundaries of Periodic Trajectories; Local Bifurcations on the Route Over Stability Boundaries; Global Bifurcations at the Disappearance of a Saddle-Node Equilibrium States and Periodic Orbits; Bifurcations of Homoclinic Loops of Saddle Equilibrium States; Safe and Dangerous Boundaries. Readership: Engineers, students, mathematicians and researchers in nonlinear dynamics and dynamical systems.

Qualitative Theory Of Dynamical Systems

Qualitative Theory Of Dynamical Systems PDF Author: Dingjun Luo
Publisher: World Scientific
ISBN: 9814504602
Category : Science
Languages : en
Pages : 275

Get Book Here

Book Description
This book deals with the global qualitative behavior of flows and diffeomorphisms. It presents a systematic study of the fundamental theory and method of dynamical systems, from local behavior near a critical (fixed) point or periodic orbit to the global, such as global structural stability, bifurcations and chaos. It emphasizes the global non-hyperbolicity and introduces some new results obtained by Chinese mathematicians which may not be widely known.

Chaos in Discrete Dynamical Systems

Chaos in Discrete Dynamical Systems PDF Author: Ralph Abraham
Publisher: Springer Science & Business Media
ISBN: 1461219361
Category : Mathematics
Languages : en
Pages : 257

Get Book Here

Book Description
The materials in the book and on the accompanying disc are not solely developed with only the researcher and professional in mind, but also with consideration for the student: most of this material has been class-tested by the authors. The book is packed with some 100 computer graphics to illustrate the material, and the CD-ROM contains full-colour animations tied directly to the subject matter of the book itself. The cross-platform CD also contains the program ENDO, which enables users to create their own 2-D imagery with X-Windows. Maple scripts are provided to allow readers to work directly with the code from which the graphics in the book were taken.

Chaos

Chaos PDF Author: Angelo Vulpiani
Publisher: World Scientific
ISBN: 9814277665
Category : Mathematics
Languages : en
Pages : 482

Get Book Here

Book Description
Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology. The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations. The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses. Sample Chapter(s). Introduction (164 KB). Chapter 1: First Encounter with Chaos (1,323 KB). Contents: First Encounter with Chaos; The Language of Dynamical Systems; Examples of Chaotic Behaviors; Probabilistic Approach to Chaos; Characterization of Chaotic Dynamical Systems; From Order to Chaos in Dissipative Systems; Chaos in Hamiltonian Systems; Chaos and Information Theory; Coarse-Grained Information and Large Scale Predictability; Chaos in Numerical and Laboratory Experiments; Chaos in Low Dimensional Systems; Spatiotemporal Chaos; Turbulence as a Dynamical System Problem; Chaos and Statistical Mechanics: Fermi-Pasta-Ulam a Case Study. Readership: Students and researchers in science (physics, chemistry, mathematics, biology) and engineering.

The Qualitative Theory of Ordinary Differential Equations

The Qualitative Theory of Ordinary Differential Equations PDF Author: Fred Brauer
Publisher: Courier Corporation
ISBN: 0486151514
Category : Mathematics
Languages : en
Pages : 325

Get Book Here

Book Description
Superb, self-contained graduate-level text covers standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters. Focuses on stability theory and its applications to oscillation phenomena, self-excited oscillations, more. Includes exercises.

Instabilities, Chaos and Turbulence

Instabilities, Chaos and Turbulence PDF Author: Paul Manneville
Publisher: World Scientific
ISBN: 9781860944833
Category : Science
Languages : en
Pages : 416

Get Book Here

Book Description
This book is an introduction to the application of nonlinear dynamics to problems of stability, chaos and turbulence arising in continuous media and their connection to dynamical systems. With an emphasis on the understanding of basic concepts, it should be of interest to nearly any science-oriented undergraduate and potentially to anyone who wants to learn about recent advances in the field of applied nonlinear dynamics. Technicalities are, however, not completely avoided. They are instead explained as simply as possible using heuristic arguments and specific worked examples.