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Author : David N. Cheban
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Kind : eBook
Book Rating : 576/5 ( reviews)
Book Synopsis Monotone Nonautonomous Dynamical Systems by : David N. Cheban
Download or read book Monotone Nonautonomous Dynamical Systems written by David N. Cheban. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt:
Author : David N Cheban
Release : 2014-12-15
Genre : Mathematics
Kind : eBook
Book Rating : 841/5 ( reviews)
Book Synopsis Global Attractors Of Non-autonomous Dynamical And Control Systems (2nd Edition) by : David N Cheban
Download or read book Global Attractors Of Non-autonomous Dynamical And Control Systems (2nd Edition) written by David N Cheban. This book was released on 2014-12-15. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Peter Kloeden
Release : 2020-11-25
Genre : Mathematics
Kind : eBook
Book Rating : 671/5 ( reviews)
Book Synopsis An Introduction To Nonautonomous Dynamical Systems And Their Attractors by : Peter Kloeden
Download or read book An Introduction To Nonautonomous Dynamical Systems And Their Attractors written by Peter Kloeden. This book was released on 2020-11-25. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : David N. Cheban
Release : 2004
Genre : Mathematics
Kind : eBook
Book Rating : 289/5 ( reviews)
Book Synopsis Global Attractors of Non-autonomous Dissipative Dynamical Systems by : David N. Cheban
Download or read book Global Attractors of Non-autonomous Dissipative Dynamical Systems written by David N. Cheban. This book was released on 2004. Available in PDF, EPUB and Kindle. Book excerpt: - The book is intended to the experts in qualitative theory of differential equations, dynamical systems and their applications
Author : David N Cheban
Release : 2004-11-29
Genre : Mathematics
Kind : eBook
Book Rating : 866/5 ( reviews)
Book Synopsis Global Attractors Of Nonautonomous Dissipative Dynamical Systems by : David N Cheban
Download or read book Global Attractors Of Nonautonomous Dissipative Dynamical Systems written by David N Cheban. This book was released on 2004-11-29. Available in PDF, EPUB and Kindle. Book excerpt: 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.
