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Stability Theory Of Differential Equations
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Book Synopsis Stability Theory of Differential Equations by : Richard Bellman
Download or read book Stability Theory of Differential Equations written by Richard Bellman and published by Courier Corporation. This book was released on 2013-02-20 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies. The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory from the beginning. In regard to the stability of nonlinear systems, results of the linear theory are used to drive the results of Poincaré and Liapounoff. Professor Bellman then surveys important results concerning the boundedness, stability, and asymptotic behavior of second-order linear differential equations. The final chapters explore significant nonlinear differential equations whose solutions may be completely described in terms of asymptotic behavior. Only real solutions of real equations are considered, and the treatment emphasizes the behavior of these solutions as the independent variable increases without limit.
Book Synopsis Ordinary Differential Equations and Stability Theory: by : David A. Sanchez
Download or read book Ordinary Differential Equations and Stability Theory: written by David A. Sanchez and published by Courier Dover Publications. This book was released on 2019-09-18 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief modern introduction to the subject of ordinary differential equations emphasizes stability theory. Concisely and lucidly expressed, it is intended as a supplementary text for advanced undergraduates or beginning graduate students who have completed a first course in ordinary differential equations. The author begins by developing the notions of a fundamental system of solutions, the Wronskian, and the corresponding fundamental matrix. Subsequent chapters explore the linear equation with constant coefficients, stability theory for autonomous and nonautonomous systems, and the problems of the existence and uniqueness of solutions and related topics. Problems at the end of each chapter and two Appendixes on special topics enrich the text.
Book Synopsis Stability Theory of Dynamical Systems by : N.P. Bhatia
Download or read book Stability Theory of Dynamical Systems written by N.P. Bhatia and published by Springer Science & Business Media. This book was released on 2002-01-10 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reprint of classic reference work. Over 400 books have been published in the series Classics in Mathematics, many remain standard references for their subject. All books in this series are reissued in a new, inexpensive softcover edition to make them easily accessible to younger generations of students and researchers. "... The book has many good points: clear organization, historical notes and references at the end of every chapter, and an excellent bibliography. The text is well-written, at a level appropriate for the intended audience, and it represents a very good introduction to the basic theory of dynamical systems."
Book Synopsis Studies in Non-Linear Stability Theory by : Wiktor Eckhaus
Download or read book Studies in Non-Linear Stability Theory written by Wiktor Eckhaus and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-linear stability problems formulated in terms of non-linear partial differential equations have only recently begun to attract attention and it will probably take some time before our understanding of those problems reaches some degree of maturity. The passage from the more classical linear analysis to a non-linear analysis increases the mathematical complexity of the stability theory to a point where it may become discouraging, while some of the more usual mathematical methods lose their applicability. Although considerable progress has been made in recent years, notably in the field of fluid mechanics, much still remains to be done before a more permanent outline of the subject can be established. I have not tried to present in this monograph an account of what has been accomplished, since the rapidly changing features of the field make the periodical literature a more appropriate place for such a review. The aim of this book is to present one particular line of research, originally developed in a series of papers published in 'Journal de Mecanique' 1962-1963, in which I attempted to construct a mathematical theory for certain classes of non-linear stability problems, and to gain some understanding of the non-linear phenomena which are involved. The opportunity to collect the material in this volume has permitted a more coherent presentation, while various points of the analysis have been developed in greater detaiL I hope that a more unified form of the theory has thus been achieved.
Book Synopsis Stability of Nonautonomous Differential Equations by : Luis Barreira
Download or read book Stability of Nonautonomous Differential Equations written by Luis Barreira and published by Springer. This book was released on 2007-09-26 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers the stability of nonautonomous differential equations in Banach spaces in the presence of nonuniform hyperbolicity. Topics under discussion include the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, and the construction and regularity of topological conjugacies. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.
Book Synopsis Theory of Integro-Differential Equations by : V. Lakshmikantham
Download or read book Theory of Integro-Differential Equations written by V. Lakshmikantham and published by CRC Press. This book was released on 1995-03-15 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique monograph investigates the theory and applications of Volterra integro-differential equations. Whilst covering the basic theory behind these equations it also studies their qualitative properties and discusses a large number of applications. This comprehensive work presents a unified framework to investigate the fundamental existence of theory, treats stability theory in terms of Lyapunov functions and functionals, develops the theory of integro-differential equations with impulse effects, and deals with linear evolution equations in abstract spaces. Various applications of integro-differential equations, such as population dynamics, nuclear reactors, viscoelasticity, wave propagation and engineering systems, are discussed, making this book indispensable for mathematicians and engineers alike.
Book Synopsis Stability, Instability and Chaos by : Paul Glendinning
Download or read book Stability, Instability and Chaos written by Paul Glendinning and published by Cambridge University Press. This book was released on 1994-11-25 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to nonlinear differential equations which equips undergraduate students with the know-how to appreciate stability theory and bifurcation.
Download or read book Differential Equations written by Halanay and published by Academic Press. This book was released on 1966-01-01 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Equations
Book Synopsis Stability of Linear Delay Differential Equations by : Dimitri Breda
Download or read book Stability of Linear Delay Differential Equations written by Dimitri Breda and published by Springer. This book was released on 2014-10-21 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the authors' recent work on the numerical methods for the stability analysis of linear autonomous and periodic delay differential equations, which consist in applying pseudospectral techniques to discretize either the solution operator or the infinitesimal generator and in using the eigenvalues of the resulting matrices to approximate the exact spectra. The purpose of the book is to provide a complete and self-contained treatment, which includes the basic underlying mathematics and numerics, examples from population dynamics and engineering applications, and Matlab programs implementing the proposed numerical methods. A number of proofs is given to furnish a solid foundation, but the emphasis is on the (unifying) idea of the pseudospectral technique for the stability analysis of DDEs. It is aimed at advanced students and researchers in applied mathematics, in dynamical systems and in various fields of science and engineering, concerned with delay systems. A relevant feature of the book is that it also provides the Matlab codes to encourage the readers to experience the practical aspects. They could use the codes to test the theory and to analyze the performances of the methods on the given examples. Moreover, they could easily modify them to tackle the numerical stability analysis of their own delay models.
Book Synopsis Stability Analysis of Impulsive Functional Differential Equations by : Ivanka Stamova
Download or read book Stability Analysis of Impulsive Functional Differential Equations written by Ivanka Stamova and published by Walter de Gruyter. This book was released on 2009-10-16 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to impulsive functional differential equations which are a natural generalization of impulsive ordinary differential equations (without delay) and of functional differential equations (without impulses). At the present time the qualitative theory of such equations is under rapid development. After a presentation of the fundamental theory of existence, uniqueness and continuability of solutions, a systematic development of stability theory for that class of problems is given which makes the book unique. It addresses to a wide audience such as mathematicians, applied researches and practitioners.
Book Synopsis Asymptotic Behavior and Stability Problems in Ordinary Differential Equations by : Lamberto Cesari
Download or read book Asymptotic Behavior and Stability Problems in Ordinary Differential Equations written by Lamberto Cesari and published by Springer. This book was released on 2013-11-09 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last few decades the theory of ordinary differential equations has grown rapidly under the action of forces which have been working both from within and without: from within, as a development and deepen ing of the concepts and of the topological and analytical methods brought about by LYAPUNOV, POINCARE, BENDIXSON, and a few others at the turn of the century; from without, in the wake of the technological development, particularly in communications, servomechanisms, auto matic controls, and electronics. The early research of the authors just mentioned lay in challenging problems of astronomy, but the line of thought thus produced found the most impressive applications in the new fields. The body of research now accumulated is overwhelming, and many books and reports have appeared on one or another of the multiple aspects of the new line of research which some authors call "qualitative theory of differential equations". The purpose of the present volume is to present many of the view points and questions in a readable short report for which completeness is not claimed. The bibliographical notes in each section are intended to be a guide to more detailed expositions and to the original papers. Some traditional topics such as the Sturm comparison theory have been omitted. Also excluded were all those papers, dealing with special differential equations motivated by and intended for the applications.
Book Synopsis Stability by Fixed Point Theory for Functional Differential Equations by : T. A. Burton
Download or read book Stability by Fixed Point Theory for Functional Differential Equations written by T. A. Burton and published by Courier Corporation. This book was released on 2013-04-16 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first general introduction to stability of ordinary and functional differential equations by means of fixed point techniques, this text is suitable for advanced undergraduates and graduate students. 2006 edition.
Book Synopsis Stochastic Stability of Differential Equations by : Rafail Khasminskii
Download or read book Stochastic Stability of Differential Equations written by Rafail Khasminskii and published by Springer Science & Business Media. This book was released on 2011-09-20 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of the first edition of the present volume in 1980, the stochastic stability of differential equations has become a very popular subject of research in mathematics and engineering. To date exact formulas for the Lyapunov exponent, the criteria for the moment and almost sure stability, and for the existence of stationary and periodic solutions of stochastic differential equations have been widely used in the literature. In this updated volume readers will find important new results on the moment Lyapunov exponent, stability index and some other fields, obtained after publication of the first edition, and a significantly expanded bibliography. This volume provides a solid foundation for students in graduate courses in mathematics and its applications. It is also useful for those researchers who would like to learn more about this subject, to start their research in this area or to study the properties of concrete mechanical systems subjected to random perturbations.
Book Synopsis Stability of Infinite Dimensional Stochastic Differential Equations with Applications by : Kai Liu
Download or read book Stability of Infinite Dimensional Stochastic Differential Equations with Applications written by Kai Liu and published by CRC Press. This book was released on 2005-08-23 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability. While the theory of such equations is well establ
Book Synopsis Hyers-Ulam Stability of Ordinary Differential Equations by : Arun Kumar Tripathy
Download or read book Hyers-Ulam Stability of Ordinary Differential Equations written by Arun Kumar Tripathy and published by CRC Press. This book was released on 2021-05-24 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hyers-Ulam Stability of Ordinary Differential Equations undertakes an interdisciplinary, integrative overview of a kind of stability problem unlike the existing so called stability problem for Differential equations and Difference Equations. In 1940, S. M. Ulam posed the problem: When can we assert that approximate solution of a functional equation can be approximated by a solution of the corresponding equation before the audience at the University of Wisconsin which was first answered by D. H. Hyers on Banach space in 1941. Thereafter, T. Aoki, D. H. Bourgin and Th. M. Rassias improved the result of Hyers. After that many researchers have extended the Ulam's stability problems to other functional equations and generalized Hyer's result in various directions. Last three decades, this topic is very well known as Hyers-Ulam Stability or sometimes it is referred Hyers-Ulam-Rassias Stability. This book synthesizes interdisciplinary theory, definitions and examples of Ordinary Differential and Difference Equations dealing with stability problems. The purpose of this book is to display the new kind of stability problem to global audience and accessible to a broader interdisciplinary readership for e.g those are working in Mathematical Biology Modeling, bending beam problems of mechanical engineering also, some kind of models in population dynamics. This book may be a starting point for those associated in such research and covers the methods needed to explore the analysis. Features: The state-of-art is pure analysis with background functional analysis. A rich, unique synthesis of interdisciplinary findings and insights on resources. As we understand that the real world problem is heavily involved with Differential and Difference equations, the cited problems of this book may be useful in a greater sense as long as application point of view of this Hyers-Ulam Stability theory is concerned. Information presented in an accessible way for students, researchers, scientists and engineers.
Author :Sergei Yurievitch Pilyugin Publisher :Springer Science & Business Media ISBN 13 :9783764325749 Total Pages :208 pages Book Rating :4.3/5 (257 download)
Book Synopsis Introduction to Structurally Stable Systems of Differential Equations by : Sergei Yurievitch Pilyugin
Download or read book Introduction to Structurally Stable Systems of Differential Equations written by Sergei Yurievitch Pilyugin and published by Springer Science & Business Media. This book was released on 1992 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Flows and Cascades.- 2. Equivalence Relations.- 3. Spaces of Systems of Differential Equations and of Diffeomorphisms.- 4. Hyperbolic Rest Point.- 5. Periodic Point and Closed Trajectory.- 6. Transversality.- 7. The Kupka-Smale Theorem.- 8. The Closing Lemma.- 9. Necessary Conditions for Structural Stability.- 10. Homoclinic Point.- 11. Morse-Smale Systems.- 12. Hyperbolic Sets.- 13. The Analytic Strong Transversality Condition.- Appendix. Proof of the Grobman-Hartman Theorem.- References.
Book Synopsis Applied Theory of Functional Differential Equations by : V. Kolmanovskii
Download or read book Applied Theory of Functional Differential Equations written by V. Kolmanovskii and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an introduction to the properties of functional differential equations and their applications in diverse fields such as immunology, nuclear power generation, heat transfer, signal processing, medicine and economics. In particular, it deals with problems and methods relating to systems having a memory (hereditary systems). The book contains eight chapters. Chapter 1 explains where functional differential equations come from and what sort of problems arise in applications. Chapter 2 gives a broad introduction to the basic principle involved and deals with systems having discrete and distributed delay. Chapters 3-5 are devoted to stability problems for retarded, neutral and stochastic functional differential equations. Problems of optimal control and estimation are considered in Chapters 6-8. For applied mathematicians, engineers, and physicists whose work involves mathematical modeling of hereditary systems. This volume can also be recommended as a supplementary text for graduate students who wish to become better acquainted with the properties and applications of functional differential equations.
