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Author : Lynn D. Maruska
Publisher :
ISBN 13 :
Total Pages : 46 pages
Book Rating : 4.:/5 (544 download)
Download or read book Stability in Autonomous Systems of Differential Equations written by Lynn D. Maruska and published by . This book was released on 1966 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Luis Barreira
Publisher : Springer
ISBN 13 : 3540747753
Total Pages : 288 pages
Book Rating : 4.5/5 (47 download)
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.
Author : Robert Jerome Rath
Publisher :
ISBN 13 :
Total Pages : 120 pages
Book Rating : 4.:/5 (111 download)
Download or read book Eventual Stability of Non-autonomous Systems of Differential Equations written by Robert Jerome Rath and published by . This book was released on 1962 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David A. Sanchez
Publisher : Courier Dover Publications
ISBN 13 : 0486837599
Total Pages : 179 pages
Book Rating : 4.4/5 (868 download)
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.
Author : Solomon Lefschetz
Publisher : Princeton University Press
ISBN 13 : 1400882176
Total Pages : 296 pages
Book Rating : 4.4/5 (8 download)
Download or read book Contributions to the Theory of Nonlinear Oscillations (AM-36), Volume III written by Solomon Lefschetz and published by Princeton University Press. This book was released on 2016-03-02 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-36), Volume III, will be forthcoming.
Author : Urabe
Publisher : Academic Press
ISBN 13 : 008095541X
Total Pages : 343 pages
Book Rating : 4.0/5 (89 download)
Download or read book Nonlinear Autonomous Oscillations: Analytical Theory written by Urabe and published by Academic Press. This book was released on 1967-01-01 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Autonomous Oscillations presents a self-contained and readable account for mathematicians, physicists, and engineers. This monograph is mainly concerned with the analytical theory of nonlinear autonomous oscillations, with the approach based mostly on the author's work. After some introductory material, in Chapter 5 a moving orthogonal coordinate system along a closed orbit is introduced. In the next four chapters, stability theory and perturbation theory are systematically discussed for general autonomous systems by means of a moving coordinate system. In Chapter 10, the two-dimensional autonomous system is discussed in detail on the basis of results obtained in the preceding chapters. In Chapter 11, a numerical method for determining a periodic solution of the general nonlinear autonomous system is described. To illustrate this, the periodic solutions of the autonomous van der Pol equation for various values of thedamping coefficient are computed. Chapter 12, which is based on the work of the author and Sibuya, discusses the center of higher dimension. Chapter 13 discusses a particular inverse problem connected with the period of periodicsolutions of one interesting equation. There are, of course, many other topics of importance in the theory of nonlinear autonomous oscillations. These are, however, omitted in the present monograph because they are mainly topological rather than analytical and in order to keep the book from growing inordinately long.
Author : J. P. LaSalle
Publisher : SIAM
ISBN 13 : 9781611970432
Total Pages : 81 pages
Book Rating : 4.9/5 (74 download)
Download or read book The Stability of Dynamical Systems written by J. P. LaSalle and published by SIAM. This book was released on 1976-01-01 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to aspects of the theory of dynamial systems based on extensions of Liapunov's direct method. The main ideas and structure for the theory are presented for difference equations and for the analogous theory for ordinary differential equations and retarded functional differential equations. The latest results on invariance properties for non-autonomous time-varying systems processes are presented for difference and differential equations.
Author : S.Y. Pilyugin
Publisher : Birkhäuser
ISBN 13 : 3034886438
Total Pages : 194 pages
Book Rating : 4.0/5 (348 download)
Download or read book Introduction to Structurally Stable Systems of Differential Equations written by S.Y. Pilyugin and published by Birkhäuser. This book was released on 2012-12-06 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a one year course of lectures on structural sta bility of differential equations which the author has given for the past several years at the Department of Mathematics and Mechanics at the University of Leningrad. The theory of structural stability has been developed intensively over the last 25 years. This theory is now a vast domain of mathematics, having close relations to the classical qualitative theory of differential equations, to differential topology, and to the analysis on manifolds. Evidently it is impossible to present a complete and detailed account of all fundamental results of the theory during a one year course. So the purpose of the course of lectures (and also the purpose of this book) was more modest. The author was going to give an introduction to the language of the theory of structural stability, to formulate its principal results, and to introduce the students (and also the readers of the book) to some of the main methods of this theory. One can select two principal aspects of modern theory of structural stability (of course there are some conventions attached to this state ment). The first one, let us call it the "geometric" aspect, deals mainly with the description of the picture of trajectories of a system; and the second, let us say the "analytic" one, has in its centre the method for solving functional equations to find invariant manifolds, conjugating homeomorphisms, and so forth.
Author : Dimitri Breda
Publisher : Springer
ISBN 13 : 149392107X
Total Pages : 162 pages
Book Rating : 4.4/5 (939 download)
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.
Author : Izhar-Ul Haq Mufti
Publisher :
ISBN 13 :
Total Pages : 144 pages
Book Rating : 4.:/5 (66 download)
Download or read book Stability in the Large of Autonomous Systems of Two Differential Equations written by Izhar-Ul Haq Mufti and published by . This book was released on 1960 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : K. Gopalsamy
Publisher : Springer Science & Business Media
ISBN 13 : 9401579202
Total Pages : 514 pages
Book Rating : 4.4/5 (15 download)
Download or read book Stability and Oscillations in Delay Differential Equations of Population Dynamics written by K. Gopalsamy and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a definitive overview of recent advances in the stability and oscillation of autonomous delay differential equations. Topics include linear and nonlinear delay and integrodifferential equations, which have potential applications to both biological and physical dynamic processes. Chapter 1 deals with an analysis of the dynamical characteristics of the delay logistic equation, and a number of techniques and results relating to stability, oscillation and comparison of scalar delay and integrodifferential equations are presented. Chapter 2 provides a tutorial-style introduction to the study of delay-induced Hopf bifurcation to periodicity and the related computations for the analysis of the stability of bifurcating periodic solutions. Chapter 3 is devoted to local analyses of nonlinear model systems and discusses many methods applicable to linear equations and their perturbations. Chapter 4 considers global convergence to equilibrium states of nonlinear systems, and includes oscillations of nonlinear systems about their equilibria. Qualitative analyses of both competitive and cooperative systems with time delays feature in both Chapters 3 and 4. Finally, Chapter 5 deals with recent developments in models of neutral differential equations and their applications to population dynamics. Each chapter concludes with a number of exercises and the overall exposition recommends this volume as a good supplementary text for graduate courses. For mathematicians whose work involves functional differential equations, and whose interest extends beyond the boundaries of linear stability analysis.
Author : Lamberto Cesari
Publisher : Springer
ISBN 13 : 3662403684
Total Pages : 278 pages
Book Rating : 4.6/5 (624 download)
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.
Author : Anna Capietto
Publisher : Springer
ISBN 13 : 3642329063
Total Pages : 314 pages
Book Rating : 4.6/5 (423 download)
Download or read book Stability and Bifurcation Theory for Non-Autonomous Differential Equations written by Anna Capietto and published by Springer. This book was released on 2012-12-14 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the notes from five lecture courses devoted to nonautonomous differential systems, in which appropriate topological and dynamical techniques were described and applied to a variety of problems. The courses took place during the C.I.M.E. Session "Stability and Bifurcation Problems for Non-Autonomous Differential Equations," held in Cetraro, Italy, June 19-25 2011. Anna Capietto and Jean Mawhin lectured on nonlinear boundary value problems; they applied the Maslov index and degree-theoretic methods in this context. Rafael Ortega discussed the theory of twist maps with nonperiodic phase and presented applications. Peter Kloeden and Sylvia Novo showed how dynamical methods can be used to study the stability/bifurcation properties of bounded solutions and of attracting sets for nonautonomous differential and functional-differential equations. The volume will be of interest to all researchers working in these and related fields.
Author : Michael I. Gil'
Publisher : Springer Science & Business Media
ISBN 13 : 9780792382218
Total Pages : 386 pages
Book Rating : 4.3/5 (822 download)
Download or read book Stability of Finite and Infinite Dimensional Systems written by Michael I. Gil' and published by Springer Science & Business Media. This book was released on 1998-09-30 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of Stability of Finite and Infinite Dimensional Systems is to provide new tools for specialists in control system theory, stability theory of ordinary and partial differential equations, and differential-delay equations. Stability of Finite and Infinite Dimensional Systems is the first book that gives a systematic exposition of the approach to stability analysis which is based on estimates for matrix-valued and operator-valued functions, allowing us to investigate various classes of finite and infinite dimensional systems from the unified viewpoint. This book contains solutions to the problems connected with the Aizerman and generalized Aizerman conjectures and presents fundamental results by A. Yu. Levin for the stability of nonautonomous systems having variable real characteristic roots. Stability of Finite and Infinite Dimensional Systems is intended not only for specialists in stability theory, but for anyone interested in various applications who has had at least a first-year graduate-level course in analysis.
Author : Werner Krabs
Publisher : Springer Science & Business Media
ISBN 13 : 3642137229
Total Pages : 245 pages
Book Rating : 4.6/5 (421 download)
Download or read book Dynamical Systems written by Werner Krabs and published by Springer Science & Business Media. This book was released on 2010-08-03 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the end of the nineteenth century Lyapunov and Poincaré developed the so called qualitative theory of differential equations and introduced geometric- topological considerations which have led to the concept of dynamical systems. In its present abstract form this concept goes back to G.D. Birkhoff. This is also the starting point of Chapter 1 of this book in which uncontrolled and controlled time-continuous and time-discrete systems are investigated. Controlled dynamical systems could be considered as dynamical systems in the strong sense, if the controls were incorporated into the state space. We, however, adapt the conventional treatment of controlled systems as in control theory. We are mainly interested in the question of controllability of dynamical systems into equilibrium states. In the non-autonomous time-discrete case we also consider the problem of stabilization. We conclude with chaotic behavior of autonomous time discrete systems and actual real-world applications.
Author : Victor A. Galaktionov
Publisher : Springer Science & Business Media
ISBN 13 : 1461220505
Total Pages : 388 pages
Book Rating : 4.4/5 (612 download)
Download or read book A Stability Technique for Evolution Partial Differential Equations written by Victor A. Galaktionov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Introduces a state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations. * Written by established mathematicians at the forefront of their field, this blend of delicate analysis and broad application is ideal for a course or seminar in asymptotic analysis and nonlinear PDEs. * Well-organized text with detailed index and bibliography, suitable as a course text or reference volume.
Author :
Publisher : Springer Science & Business Media
ISBN 13 : 0817644865
Total Pages : 516 pages
Book Rating : 4.8/5 (176 download)
Download or read book Stability of Dynamical Systems written by and published by Springer Science & Business Media. This book was released on 2008 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the analysis and synthesis of contemporary systems, engineers and scientists are frequently confronted with increasingly complex models that may simultaneously include components whose states evolve along continuous time and discrete instants; components whose descriptions may exhibit nonlinearities, time lags, transportation delays, hysteresis effects, and uncertainties in parameters; and components that cannot be described by various classical equations, as in the case of discrete-event systems, logic commands, and Petri nets. The qualitative analysis of such systems requires results for finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time systems; and hybrid systems involving a mixture of continuous and discrete dynamics. Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of all the major types of system models described above. Throughout the book, the applicability of the developed theory is demonstrated by means of many specific examples and applications to important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, artificial neural networks (with and without time delays), digital signal processing, a class of discrete-event systems (with applications to manufacturing and computer load balancing problems) and a multicore nuclear reactor model. The book covers the following four general topics: * Representation and modeling of dynamical systems of the types described above * Presentation of Lyapunov and Lagrange stability theory for dynamical systems defined on general metric spaces * Specialization of this stability theory to finite-dimensional dynamical systems * Specialization of this stability theory to infinite-dimensional dynamical systems Replete with exercises and requiring basic knowledge of linear algebra, analysis, and differential equations, the work may be used as a textbook for graduate courses in stability theory of dynamical systems. The book may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, physics, chemistry, biology, and economics.
