Stability Of Nonautonomous Differential Equations

Author : Luis Barreira
Publisher : Springer
ISBN 13 : 3540747753
Total Pages : 291 pages
Book Rating : 4.58/5 ( download)

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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 291 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 : Yu. A. Mitropolsky
Publisher : CRC Press
ISBN 13 : 1482264897
Total Pages : 400 pages
Book Rating : 4.90/5 ( download)

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Download or read book Dichotomies and Stability in Nonautonomous Linear Systems written by Yu. A. Mitropolsky and published by CRC Press. This book was released on 2002-10-10 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear nonautonomous equations arise as mathematical models in mechanics, chemistry, and biology. The investigation of bounded solutions to systems of differential equations involves some important and challenging problems of perturbation theory for invariant toroidal manifolds. This monograph is a detailed study of the application of Lyapunov func

Author : Junji Kato
Publisher : Routledge
ISBN 13 : 1351414860
Total Pages : 304 pages
Book Rating : 4.69/5 ( download)

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Download or read book Stability of Motion of Nonautonomous Systems (Methods of Limiting Equations) written by Junji Kato and published by Routledge. This book was released on 2019-09-09 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuing the strong tradition of functional analysis and stability theory for differential and integral equations already established by the previous volumes in this series, this innovative monograph considers in detail the method of limiting equations constructed in terms of the Bebutov-Miller-Sell concept, the method of comparison, and Lyapunov's direct method based on scalar, vector and matrix functions. The stability of abstract compacted and uniform dynamic processes, dispersed systems and evolutionary equations in Banach space are also discussed. For the first time, the method first employed by Krylov and Bogolubov in their investigations of oscillations in almost linear systems is applied to a new field: that of the stability problem of systems with small parameters. This important development should facilitate the solution of engineering problems in such areas as orbiting satellites, rocket motion, high-speed vehicles, power grids, and nuclear reactors.

Author : David N. Cheban
Publisher : Nova Science Publishers
ISBN 13 : 9781626189263
Total Pages : 0 pages
Book Rating : 4.69/5 ( download)

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Download or read book Lyapunov Stability of Non-autonomous Dynamical Systems written by David N. Cheban and published by Nova Science Publishers. This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The foundation of the modern theory of stability was created in the works of A Poincare and A M Lyapunov. The theory of the stability of motion has gained increasing significance in the last decade as is apparent from the large number of publications on the subject. A considerable part of these works are concerned with practical problems, especially problems from the area of controls and servo-mechanisms, and concrete problems from engineering, which first gave the decisive impetus for the expansion and modern development of stability theory. This book contains a systematic exposition of the elements of the asymptotic stability theory of general non-autonomous dynamical systems in metric spaces with an emphasis on the application for different classes of non-autonomous evolution equations (Ordinary Differential Equations (ODEs), Difference Equations (DEs), Functional-Differential Equations (FDEs), Semi-Linear Parabolic Equations etc). The basic results of this book are contained in the courses of lectures which the author has given during many years for the students of the State University of Moldova.This book is intended for mathematicians (scientists and university professors) who are working in the field of stability theory of differential/difference equations, dynamical systems and control theory. It would also be of use for the graduate and post graduate student who is interested in the theory of dynamical systems and its applications. The reader needs no deep knowledge of special branches of mathematics, although it should be easier for readers who know the fundamentals concepts of the theory of metric spaces, qualitative theory of differential/difference equations and dynamical systems.

Author : David A. Sanchez
Publisher : Courier Dover Publications
ISBN 13 : 0486837599
Total Pages : 179 pages
Book Rating : 4.98/5 ( download)

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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 : Peter E. Kloeden
Publisher : American Mathematical Soc.
ISBN 13 : 0821868713
Total Pages : 274 pages
Book Rating : 4.13/5 ( download)

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Download or read book Nonautonomous Dynamical Systems written by Peter E. Kloeden and published by American Mathematical Soc.. This book was released on 2011-08-17 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of nonautonomous dynamical systems in both of its formulations as processes and skew product flows is developed systematically in this book. The focus is on dissipative systems and nonautonomous attractors, in particular the recently introduced concept of pullback attractors. Linearization theory, invariant manifolds, Lyapunov functions, Morse decompositions and bifurcations for nonautonomous systems and set-valued generalizations are also considered as well as applications to numerical approximations, switching systems and synchronization. Parallels with corresponding theories of control and random dynamical systems are briefly sketched. With its clear and systematic exposition, many examples and exercises, as well as its interesting applications, this book can serve as a text at the beginning graduate level. It is also useful for those who wish to begin their own independent research in this rapidly developing area.

Author : Anna Capietto
Publisher : Springer
ISBN 13 : 3642329063
Total Pages : 314 pages
Book Rating : 4.67/5 ( download)

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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 : J. P. LaSalle
Publisher : SIAM
ISBN 13 : 9781611970432
Total Pages : 81 pages
Book Rating : 4.31/5 ( download)

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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 : David N. Cheban
Publisher : Springer Nature
ISBN 13 : 3030342921
Total Pages : 434 pages
Book Rating : 4.20/5 ( download)

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Download or read book Nonautonomous Dynamics written by David N. Cheban and published by Springer Nature. This book was released on 2020-01-22 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes those topological methods (of dynamical systems) and theories that are useful in the study of different classes of nonautonomous evolutionary equations. The content is developed over six chapters, providing a thorough introduction to the techniques used in the Chapters III-VI described by Chapter I-II. The author gives a systematic treatment of the basic mathematical theory and constructive methods for Nonautonomous Dynamics. They show how these diverse topics are connected to other important parts of mathematics, including Topology, Functional Analysis and Qualitative Theory of Differential/Difference Equations. Throughout the book a nice balance is maintained between rigorous mathematics and applications (ordinary differential/difference equations, functional differential equations and partial difference equations). The primary readership includes graduate and PhD students and researchers in in the field of dynamical systems and their applications (control theory, economic dynamics, mathematical theory of climate, population dynamics, oscillation theory etc).

Author : Junji Kato
Publisher : CRC Press
ISBN 13 : 9780367455965
Total Pages : 304 pages
Book Rating : 4.6X/5 ( download)

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Download or read book Stability of Motion of Nonautonomous Systems written by Junji Kato and published by CRC Press. This book was released on 2019-11-25 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuing the strong tradition of functional analysis and stability theory for differential and integral equations already established by the previous volumes in this series, this innovative monograph considers in detail the method of limiting equations constructed in terms of the Bebutov-Miller-Sell concept, the method of comparison, and Lyapunov's direct method based on scalar, vector and matrix functions. The stability of abstract compacted and uniform dynamic processes, dispersed systems and evolutionary equations in Banach space are also discussed. For the first time, the method first employed by Krylov and Bogolubov in their investigations of oscillations in almost linear systems is applied to a new field: that of the stability problem of systems with small parameters. This important development should facilitate the solution of engineering problems in such areas as orbiting satellites, rocket motion, high-speed vehicles, power grids, and nuclear reactors.