Lyapunov Stability Of Non Autonomous Dynamical Systems
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Lyapunov Stability Of Non Autonomous Dynamical Systems
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Author : David N. Cheban
language : en
Publisher: Nova Science Publishers
Release Date : 2013
Lyapunov Stability Of Non Autonomous Dynamical Systems written by David N. Cheban and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Lyapunov stability categories.
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.
Stability Of Nonautonomous Differential Equations
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Author : Luis Barreira
language : en
Publisher: Springer
Release Date : 2007-09-26
Stability Of Nonautonomous Differential Equations written by Luis Barreira and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-26 with Mathematics categories.
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.
Nonautonomous Dynamical Systems
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Author : Peter E. Kloeden
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-08-17
Nonautonomous Dynamical Systems written by Peter E. Kloeden and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-17 with Mathematics categories.
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.
Stability And Bifurcation Theory For Non Autonomous Differential Equations
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Author : Anna Capietto
language : en
Publisher: Springer
Release Date : 2012-12-14
Stability And Bifurcation Theory For Non Autonomous Differential Equations written by Anna Capietto and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-14 with Mathematics categories.
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.
Stability Of Dynamical Systems
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Author :
language : en
Publisher: Springer Science & Business Media
Release Date : 2008
Stability Of Dynamical Systems written by and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Differentiable dynamical systems categories.
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.
Nonautonomous Dynamics
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Author : David N. Cheban
language : en
Publisher: Springer Nature
Release Date : 2020-01-22
Nonautonomous Dynamics written by David N. Cheban and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-22 with Mathematics categories.
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).
An Introduction To Nonautonomous Dynamical Systems And Their Attractors
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Author : Peter Kloeden
language : en
Publisher: World Scientific
Release Date : 2020-11-25
An Introduction To Nonautonomous Dynamical Systems And Their Attractors written by Peter Kloeden and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-25 with Mathematics categories.
The nature of time in a nonautonomous dynamical system is very different from that in autonomous systems, which depend only on the time that has elapsed since starting rather than on the actual time itself. Consequently, limiting objects may not exist in actual time as in autonomous systems. New concepts of attractors in nonautonomous dynamical system are thus required.In addition, the definition of a dynamical system itself needs to be generalised to the nonautonomous context. Here two possibilities are considered: two-parameter semigroups or processes and the skew product flows. Their attractors are defined in terms of families of sets that are mapped onto each other under the dynamics rather than a single set as in autonomous systems. Two types of attraction are now possible: pullback attraction, which depends on the behaviour from the system in the distant past, and forward attraction, which depends on the behaviour of the system in the distant future. These are generally independent of each other.The component subsets of pullback and forward attractors exist in actual time. The asymptotic behaviour in the future limit is characterised by omega-limit sets, in terms of which form what are called forward attracting sets. They are generally not invariant in the conventional sense, but are asymptotically invariant in general and, if the future dynamics is appropriately uniform, also asymptotically negatively invariant.Much of this book is based on lectures given by the authors in Frankfurt and Wuhan. It was written mainly when the first author held a 'Thousand Expert' Professorship at the Huazhong University of Science and Technology in Wuhan.
Global Attractors Of Non Autonomous Dynamical And Control Systems 2nd Edition
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Author : David N Cheban
language : en
Publisher: World Scientific
Release Date : 2014-12-15
Global Attractors Of Non Autonomous Dynamical And Control Systems 2nd Edition written by David N Cheban and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-15 with Mathematics categories.
The study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations. This engaging volume presents an authoritative overview of both autonomous and non-autonomous dynamical systems, including the global compact attractor. From an in-depth introduction to the different types of dissipativity and attraction, the book takes a comprehensive look at the connections between them, and critically discusses applications of general results to different classes of differential equations.The new Chapters 15-17 added to this edition include some results concerning Control Dynamical Systems — the global attractors, asymptotic stability of switched systems, absolute asymptotic stability of differential/difference equations and inclusions — published in the works of author in recent years.
Global Attractors Of Non Autonomous Dissipative Dynamical Systems
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Author : David N. Cheban
language : en
Publisher: World Scientific
Release Date : 2004
Global Attractors Of Non Autonomous Dissipative Dynamical Systems written by David N. Cheban and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
The study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations. This engaging volume presents an authoritative overview of both autonomous and non-autonomous dynamical systems, including the global compact attractor.
Global Attractors Of Nonautonomous Dissipative Dynamical Systems
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Author : David N Cheban
language : en
Publisher: World Scientific
Release Date : 2004-11-29
Global Attractors Of Nonautonomous Dissipative Dynamical Systems written by David N Cheban and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-29 with Mathematics categories.
The study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations. This engaging volume presents an authoritative overview of both autonomous and non-autonomous dynamical systems, including the global compact attractor. From an in-depth introduction to the different types of dissipativity and attraction, the book takes a comprehensive look at the connections between them, and critically discusses applications of general results to different classes of differential equations. Intended for experts in qualitative theory of differential equations, dynamical systems and their applications, this accessible book can also serve as an important resource for senior students and lecturers.