Описание: 1. Presentation of Main Ideas.- 2. Basic Introduction to Bifurcations in 1-D.- 3. The Other Generic Bifurcations.- 4. Classification of the 7 Elementary Catastrophes.- 5. Hopf Bifurcation.- 6. Amplitude Equation for the Hopf Bifurcation.- 7. Parametric Instabilities and Other Nonlinear Behaviors.- 8. Introduction to Chaos.- 9. Pattern Formation in One Dimension.- 10. Universality in the Vicinity of the Threshold.- 11. Fronts between Domains.- 12. Order and Disorder both Spatial and Temporal.- 13. Two Dimensional Patterns.- 14. Wavelength Selection.- 15. Conclusion.- 16. Solutions to Exercises.- Bibliography.
Описание: This book is a collection of papers contributed by some of the greatest names in the areas of chaos and nonlinear dynamics. Each paper examines a research topic at the frontier of the area of dynamical systems. As well as reviewing recent results, each paper also discusses the future perspectives of each topic. The result is an invaluable snapshot of the state of the ?eld by some of the most important researchers in the area. The ?rst contribution in this book (the section entitled "How did you get into Chaos?") is actually not a paper, but a collection of personal accounts by a number of participants of the conference held in Aberdeen in September 2007 to honour Celso Grebogi's 60th birthday. At the instigation of James Yorke, many of the most well-known scientists in the area agreed to share their tales on how they got involved in chaos during a celebratory dinner in Celso's honour during the conference. This was recorded in video, we felt that these accounts were a valuable historic document for the ?eld. So we decided to transcribe it and include it here as the ?rst section of the book.
Автор: Armin Fuchs Название: Nonlinear Dynamics in Complex Systems ISBN: 3642427812 ISBN-13(EAN): 9783642427817 Издательство: Springer Рейтинг: Цена: 9141.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Concise and accessible, this introduction to the mathematical tools of non-linear dynamics and complex systems theory is aimed at researchers in engineering and the life sciences who are unfamiliar with the formulae, but recognize their analytical potency.
Автор: Kenju Otsuka Название: Nonlinear Dynamics in Optical Complex Systems ISBN: 9048153832 ISBN-13(EAN): 9789048153831 Издательство: Springer Рейтинг: Цена: 27951.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book is the first comprehensive volume on nonlinear dynamics and chaos in optical systems.
Описание: 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.
Описание: 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.
Автор: Bhimsen K. Shivamoggi Название: Nonlinear Dynamics and Chaotic Phenomena: An Introduction ISBN: 9400770936 ISBN-13(EAN): 9789400770935 Издательство: Springer Рейтинг: Цена: 22203.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book clearly details the basic concepts, language and results of nonlinear dynamical systems. It serves as an ideal reference to first-year graduate students and theoretically inclined researchers in the physical sciences and engineering.
Автор: Wiggins, Stephen Название: Introduction to applied nonlinear dynamical systems and chaos ISBN: 1441918078 ISBN-13(EAN): 9781441918079 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior.
Описание: This volume is intended for advanced undergraduate or first-year graduate students as an introduction to applied nonlinear dynamics and chaos. The author has placed emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about the behavior of these systems. He has included the basic core material that is necessary for higher levels of study and research. Thus, people who do not necessarily have an extensive mathematical background, such as students in engineering, physics, chemistry, and biology, will find this text as useful as students of mathematics. This new edition contains extensive new material on invariant manifold theory and normal forms (in particular, Hamiltonian normal forms and the role of symmetry). Lagrangian, Hamiltonian, gradient, and reversible dynamical systems are also discussed. Elementary Hamiltonian bifurcations are covered, as well as the basic properties of circle maps. The book contains an extensive bibliography as well as a detailed glossary of terms, making it a comprehensive book on applied nonlinear dynamical systems from a geometrical and analytical point of view.
Автор: Strogatz Steven Название: Nonlinear Dynamics and Chaos ISBN: 0813349109 ISBN-13(EAN): 9780813349107 Издательство: Taylor&Francis Рейтинг: Цена: 10564.00 р. Наличие на складе: Нет в наличии.
Описание: 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.A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory.In the twenty years since the first edition of this book appeared, the ideas and techniques of nonlinear dynamics and chaos have found application to such exciting new fields as systems biology, evolutionary game theory, and sociophysics. This second edition includes new exercises on these cutting-edge developments, on topics as varied as the curiosities of visual perception and the tumultuous love dynamics in Gone With the Wind .
Описание: There is no recent elementary introduction to the theory of discrete dynamical systems that stresses the topological background of the topic. This book fills this gap: it deals with this theory as 'applied general topology'. We treat all important concepts needed to understand recent literature. The book is addressed primarily to graduate students. The prerequisites for understanding this book are modest: a certain mathematical maturity and course in General Topology are sufficient.
Описание: Treats the dynamics of both iteration of functions and solutions of ordinary differential equations. This book introduces various concepts for iteration of functions where the geometry is simpler, but results are interpreted for differential equations. It concentrates on properties of the whole system or subsets of the system.
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