Monotone Nonautonomous Dynamical Systems
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Monotone Nonautonomous Dynamical Systems
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Author : David N. Cheban
language : en
Publisher: Springer Nature
Release Date :
Monotone Nonautonomous Dynamical Systems 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 with categories.
Monotone Nonautonomous Dynamical Systems
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Author : David Cheban
language : en
Publisher: Springer
Release Date : 2024-09-16
Monotone Nonautonomous Dynamical Systems written by David Cheban and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-16 with Mathematics categories.
The monograph present ideas and methods, developed by the author, to solve the problem of existence of Bohr/Levitan almost periodic (respectively, almost recurrent in the sense of Bebutov, almost authomorphic, Poisson stable) solutions and global attractors of monotone nonautonomous differential/difference equations. Namely, the text provides answers to the following problems: 1. Problem of existence of at least one Bohr/Levitan almost periodic solution for cooperative almost periodic differential/difference equations; 2. Problem of existence of at least one Bohr/Levitan almost periodic solution for uniformly stable and dissipative monotone differential equations (I. U. Bronshtein’s conjecture, 1975); 3. Problem of description of the structure of the global attractor for monotone nonautonomous dynamical systems; 4. The structure of the invariant/minimal sets and global attractors for one-dimensional monotone nonautonomous dynamical systems; 5. Asymptotic behavior of monotone nonautonomous dynamical systems with a first integral (Poisson stable motions, convergence, asymptotically Poisson stable motions and structure of the Levinson center (compact global attractor) of dissipative systems); 6. Existence and convergence to Poisson stable motions of monotone sub-linear nonautonomous dynamical systems. This book will be interesting to the mathematical community working in the field of nonautonomous dynamical systems and their applications (population dynamics, oscillation theory, ecology, epidemiology, economics, biochemistry etc). The book should be accessible to graduate and PhD students who took courses in real analysis (including the elements of functional analysis, general topology) and with general background in dynamical systems and qualitative theory of differential/difference equations.
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.
Topological Entropy Of Nonautonomous Piecewise Monotone Dynamical Systems On The Interval
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Author : Sergiy Kolyada
language : en
Publisher:
Release Date : 1998
Topological Entropy Of Nonautonomous Piecewise Monotone Dynamical Systems On The Interval written by Sergiy Kolyada and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
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.
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.
Nonautonomous Dynamical Systems In The Life Sciences
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Author : Peter E. Kloeden
language : en
Publisher: Springer
Release Date : 2014-01-22
Nonautonomous Dynamical Systems In The Life Sciences written by Peter E. Kloeden and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-22 with Mathematics categories.
Nonautonomous dynamics describes the qualitative behavior of evolutionary differential and difference equations, whose right-hand side is explicitly time dependent. Over recent years, the theory of such systems has developed into a highly active field related to, yet recognizably distinct from that of classical autonomous dynamical systems. This development was motivated by problems of applied mathematics, in particular in the life sciences where genuinely nonautonomous systems abound. The purpose of this monograph is to indicate through selected, representative examples how often nonautonomous systems occur in the life sciences and to outline the new concepts and tools from the theory of nonautonomous dynamical systems that are now available for their investigation.
Applied Nonautonomous And Random Dynamical Systems
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Author : Tomás Caraballo
language : en
Publisher: Springer
Release Date : 2017-01-31
Applied Nonautonomous And Random Dynamical Systems written by Tomás Caraballo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-31 with Mathematics categories.
This book offers an introduction to the theory of non-autonomous and stochastic dynamical systems, with a focus on the importance of the theory in the Applied Sciences. It starts by discussing the basic concepts from the theory of autonomous dynamical systems, which are easier to understand and can be used as the motivation for the non-autonomous and stochastic situations. The book subsequently establishes a framework for non-autonomous dynamical systems, and in particular describes the various approaches currently available for analysing the long-term behaviour of non-autonomous problems. Here, the major focus is on the novel theory of pullback attractors, which is still under development. In turn, the third part represents the main body of the book, introducing the theory of random dynamical systems and random attractors and revealing how it may be a suitable candidate for handling realistic models with stochasticity. A discussion of future research directions serves to round out the coverage.
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 book is intended to the experts in qualitative theory of differential equations, dynamical systems and their applications
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.