Methods Of Qualitative Theory In Nonlinear Dynamics

Author : Leonid P Shilnikov,Andrey L Shilnikov,Dmitry V Turaev,Leon O Chua
Publisher : World Scientific
Page : 416 pages
File Size : 44,6 Mb
Release : 1998-12-08
Category : Science
ISBN : 9789814496421

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Methods of Qualitative Theory in Nonlinear Dynamics by Leonid P Shilnikov,Andrey L Shilnikov,Dmitry V Turaev,Leon O Chua Pdf

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. Contents:Basic ConceptsStructurally Stable Equilibrium States of Dynamical SystemsStructurally Stable Periodic Trajectories of Dynamical SystemsInvariant ToriCenter Manifold. Local CaseCenter Manifold. Non-Local Case Readership: Engineers, students, mathematicians and researchers in nonlinear dynamics and dynamical systems. Keywords:Bifurcations;Dynamical Systems;Qualitative Theory;Chaos;Strange Attractors;Nonlinear DynamicsReviews: “It is well-written and clearly organized with excellent figures … This rigorous book, with its emphasis on mathematical technique, would form an excellent basis for an engineering course if supplemented with applications.” Applied Mechanics Reviews “Short remarks concerning various, not only mathematical, aspects of the theory add an extra flavour to the text. I recommend the book for all persons interested in the qualitative theory of differential equations.” Mathematical Reviews

Author : Leon O Chua,Leonid P Shilnikov,Andrey L Shilnikov,Dmitry V Turaev
Publisher : World Scientific
Page : 591 pages
File Size : 49,8 Mb
Release : 2001-09-27
Category : Science
ISBN : 9789814494298

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Methods Of Qualitative Theory In Nonlinear Dynamics (Part Ii) by Leon O Chua,Leonid P Shilnikov,Andrey L Shilnikov,Dmitry V Turaev Pdf

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 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 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.

Author : L. P. Shilʹnikov
Publisher : Unknown
Page : 957 pages
File Size : 52,5 Mb
Release : 1998
Category : Nonlinear mechanics
ISBN : 9810233825

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Methods of Qualitative Theory in Nonlinear Dynamics by L. P. Shilʹnikov Pdf

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 Poincare, 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

Author : Leonid P. Shilnikov
Publisher : World Scientific
Page : 420 pages
File Size : 42,5 Mb
Release : 1998
Category : Science
ISBN : 9810233825

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Methods of Qualitative Theory in Nonlinear Dynamics by Leonid P. Shilnikov Pdf

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 Poincare, 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 studentsof nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.

Author : Leonid P. Shilnikov
Publisher : Unknown
Page : 128 pages
File Size : 51,9 Mb
Release : 2001
Category : Electronic
ISBN : OCLC:179766977

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Methods of Qualitative Theory in Nonlinear Dynamics by Leonid P. Shilnikov Pdf

Author : L. P. Shil'nikov
Publisher : World Scientific
Page : 591 pages
File Size : 54,6 Mb
Release : 2001
Category : Mathematics
ISBN : 9789812798558

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Methods of Qualitative Theory in Nonlinear Dynamics by L. P. Shil'nikov Pdf

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.

Author : Jose L. Huertas,Wai-Kai Chen,Rabinder N. Madan
Publisher : World Scientific
Page : 874 pages
File Size : 41,7 Mb
Release : 1999
Category : Science
ISBN : 981023337X

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Visions of Nonlinear Science in the 21st Century by Jose L. Huertas,Wai-Kai Chen,Rabinder N. Madan Pdf

Authoritative and visionary, this festschrift features 12 highly readable expositions of virtually all currently active aspects of nonlinear science. It has been painstakingly researched and written by leading scientists and eminent expositors, including L Shilnikov, R Seydel, I Prigogine, W Porod, C Mira, M Lakshmanan, W Lauterborn, A Holden, H Haken, C Grebogi, E Doedel and L Chua; each chapter addresses a current and intensively researched area of nonlinear science and chaos, including nonlinear dynamics, mathematics, numerics and technology. Handsomely produced with high resolution color graphics for enhanced readability, this book has been carefully written at a high level of exposition and is somewhat self-contained. Each chapter includes a tutorial and background information, as well as a survey of each area's main results and state of the art. Of special interest to both beginners and seasoned researchers is the identification of future trends and challenging yet tractable problems thatare likely,to be solved before the end of the 21st century. The visionary and provocative nature of this book makes it a valuable and lasting reference.

Author : A.A. Martynyuk
Publisher : CRC Press
Page : 320 pages
File Size : 49,5 Mb
Release : 2001-11-05
Category : Mathematics
ISBN : 9781482294743

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Qualitative Methods in Nonlinear Dynamics by A.A. Martynyuk Pdf

"Presents new approaches to qualitative analysis of continuous, discreteptime, and impulsive nonlinear systems via Liapunov matrix-valued functions that introduce more effective tests for solving problems of estimating the domains of asymptotic stability."

Author : Michael Z. Zgurovsky,Pavlo O. Kasyanov
Publisher : Springer
Page : 240 pages
File Size : 53,7 Mb
Release : 2017-07-11
Category : Technology & Engineering
ISBN : 9783319598406

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Qualitative and Quantitative Analysis of Nonlinear Systems by Michael Z. Zgurovsky,Pavlo O. Kasyanov Pdf

Here, the authors present modern methods of analysis for nonlinear systems which may occur in fields such as physics, chemistry, biology, or economics. They concentrate on the following topics, specific for such systems: (a) constructive existence results and regularity theorems for all weak solutions; (b) convergence results for solutions and their approximations; (c) uniform global behavior of solutions in time; and (d) pointwise behavior of solutions for autonomous problems with possible gaps by the phase variables. The general methodology for the investigation of dissipative dynamical systems with several applications including nonlinear parabolic equations of divergent form, nonlinear stochastic equations of parabolic type, unilateral problems, nonlinear PDEs on Riemannian manifolds with or without boundary, contact problems as well as particular examples is established. As such, the book is addressed to a wide circle of mathematical, mechanical and engineering readers.

Author : Vasile Marinca,Nicolae Herisanu,Bogdan Marinca
Publisher : Springer Nature
Page : 479 pages
File Size : 45,6 Mb
Release : 2021-07-14
Category : Technology & Engineering
ISBN : 9783030756536

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Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems by Vasile Marinca,Nicolae Herisanu,Bogdan Marinca Pdf

This book presents the optimal auxiliary functions method and applies it to various engineering problems and in particular in boundary layer problems. The cornerstone of the presented procedure is the concept of “optimal auxiliary functions” which are needed to obtain accurate results in an efficient way. Unlike other known analytic approaches, this procedure provides us with a simple but rigorous way to control and adjust the convergence of the solutions of nonlinear dynamical systems. The optimal auxiliary functions are depending on some convergence-control parameters whose optimal values are rigorously determined from mathematical point of view. The capital strength of our procedure is its fast convergence, since after only one iteration, we obtain very accurate analytical solutions which are very easy to be verified. Moreover, no simplifying hypothesis or assumptions are made. The book contains a large amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and many more. The book is a continuation of our previous books “Nonlinear Dynamical Systems in Engineering. Some Approximate Approaches”, Springer-2011 and “The Optimal Homotopy Asymptotic Method. Engineering Applications”, Springer-2015.

Author : Tong-ren Ding
Publisher : Unknown
Page : 394 pages
File Size : 40,8 Mb
Release : 2007
Category : Electronic
ISBN : 9812779817

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Approaches to the Qualitative Theory of Ordinary Differential Equations by Tong-ren Ding Pdf

Author : P.G. Bakker
Publisher : Springer Science & Business Media
Page : 221 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401135122

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Bifurcations in Flow Patterns by P.G. Bakker Pdf

The main idea of the present study is to demonstrate that the qualitative theory of diffe rential equations, when applied to problems in fluid-and gasdynamics, will contribute to the understanding of qualitative aspects of fluid flows, in particular those concerned with geometrical properties of flow fields such as shape and stability of its streamline patterns. It is obvious that insight into the qualitative structure of flow fields is of great importance and appears as an ultimate aim of flow research. Qualitative insight fashions our know ledge and serves as a good guide for further quantitative investigations. Moreover, quali tative information can become very useful, especially when it is applied in close corres pondence with numerical methods, in order to interpret and value numerical results. A qualitative analysis may be crucial for the investigation of the flow in the neighbourhood of singularities where a numerical method is not reliable anymore due to discretisation er rors being unacceptable. Up till now, familiar research methods -frequently based on rigorous analyses, careful nu merical procedures and sophisticated experimental techniques -have increased considera bly our qualitative knowledge of flows, albeit that the information is often obtained indirectly by a process of a careful but cumbersome examination of quantitative data. In the past decade, new methods are under development that yield the qualitative infor mation more directly. These methods, make use of the knowledge available in the qualitative theory of differen tial equations and in the theory of bifurcations.

Author : Leon O Chua
Publisher : World Scientific
Page : 396 pages
File Size : 46,5 Mb
Release : 2006-06-08
Category : Science
ISBN : 9789814478687

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'A Nonlinear Dynamics Perspective of Wolfram''s New Kind of Science' by Leon O Chua Pdf

' This novel book introduces cellular automata from a rigorous nonlinear dynamics perspective. It supplies the missing link between nonlinear differential and difference equations to discrete symbolic analysis. A surprisingly useful interpretations of cellular automata in terms of neural networks is also given. The book provides a scientifically sound and original analysis, and classifications of the empirical results presented in Wolfram''s monumental “New Kind of Science.” Readership: Graduate students, academics and researchers in nonlinear dynamics, computer science and complexity theory.Keywords:Cellular Automata;Nonlinear Dynamics;Wolfram;Neural Networks;Cellular Neural Networks;CNN;Universal Computation;Turing Machine;Chaos;Nonlinear Science;Complexity;Emergence "This book is a colourful presentation with fresh ideas and attractive illustrations … those studying non-linear sciences, electronic engineering, mathematics and logics, complexity and emergent phenomena, and possibly even chemistry and biology will certainly discover exciting concepts, analogies and research tools in this refreshing text. Anyone from freshmen to elderly academics will find parts interesting to them. The volumes are somewhat special and exciting because they possess a unique ''Chua brand'' and show gradual development of ideas and concepts in an educational and entertaining hence mathematically rigorous manner." Journal of Cellular Automata "There is much of interest here, and in particular many interesting examples presented in novel ways." Zentralblatt MATH '

Author : Vladimir I. Nekorkin
Publisher : John Wiley & Sons
Page : 264 pages
File Size : 41,5 Mb
Release : 2016-05-02
Category : Science
ISBN : 9783527685431

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Introduction to Nonlinear Oscillations by Vladimir I. Nekorkin Pdf

A systematic outline of the basic theory of oscillations, combining several tools in a single textbook. The author explains fundamental ideas and methods, while equally aiming to teach students the techniques of solving specific (practical) or more complex problems. Following an introduction to fundamental notions and concepts of modern nonlinear dynamics, the text goes on to set out the basics of stability theory, as well as bifurcation theory in one and two-dimensional cases. Foundations of asymptotic methods and the theory of relaxation oscillations are presented, with much attention paid to a method of mappings and its applications. With each chapter including exercises and solutions, including computer problems, this book can be used in courses on oscillation theory for physics and engineering students. It also serves as a good reference for students and scientists in computational neuroscience.

Author : Hernán González-Aguilar,Edgardo Ugalde
Publisher : Springer
Page : 240 pages
File Size : 54,9 Mb
Release : 2015-02-10
Category : Technology & Engineering
ISBN : 9783319098647

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Nonlinear Dynamics New Directions by Hernán González-Aguilar,Edgardo Ugalde Pdf

This book, along with its companion volume, Nonlinear Dynamics New Directions: Theoretical Aspects, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: · Develops applications of nonlinear dynamics on a diversity of topics such as patterns of synchrony in neuronal networks, laser synchronization, control of chaotic systems, and the study of transient dynamics in biological · Includes a study of self-organized regularity in long-range systems · Explains use of Levenstein's distance for measuring lexical evolution rates