Applied Nonautonomous And Random Dynamical Systems
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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.
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.
Introduction To Applied Nonlinear Dynamical Systems And Chaos
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Author : Stephen Wiggins
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18
Introduction To Applied Nonlinear Dynamical Systems And Chaos written by Stephen Wiggins 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 2006-04-18 with Mathematics categories.
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in - search and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as nume- cal and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mat- matical Sciences (AMS) series, whichwill focus on advanced textbooks and research-level monographs. Pasadena, California J.E. Marsden Providence, Rhode Island L. Sirovich College Park, Maryland S.S. Antman Preface to the Second Edition This edition contains a signi?cant amount of new material. The main r- son for this is that the subject of applied dynamical systems theory has seen explosive growth and expansion throughout the 1990s. Consequently, a student needs a much larger toolbox today in order to begin research on signi?cant problems.
Attractors Under Autonomous And Non Autonomous Perturbations
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Author : Matheus C. Bortolan
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-05-29
Attractors Under Autonomous And Non Autonomous Perturbations written by Matheus C. Bortolan 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 2020-05-29 with Education categories.
This book provides a comprehensive study of how attractors behave under perturbations for both autonomous and non-autonomous problems. Furthermore, the forward asymptotics of non-autonomous dynamical systems is presented here for the first time in a unified manner. When modelling real world phenomena imprecisions are unavoidable. On the other hand, it is paramount that mathematical models reflect the modelled phenomenon, in spite of unimportant neglectable influences discounted by simplifications, small errors introduced by empirical laws or measurements, among others. The authors deal with this issue by investigating the permanence of dynamical structures and continuity properties of the attractor. This is done in both the autonomous (time independent) and non-autonomous (time dependent) framework in four distinct levels of approximation: the upper semicontinuity, lower semicontinuity, topological structural stability and geometrical structural stability. This book is aimed at graduate students and researchers interested in dissipative dynamical systems and stability theory, and requires only a basic background in metric spaces, functional analysis and, for the applications, techniques of ordinary and partial differential equations.
Dissipative Lattice Dynamical Systems
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Author : Xiaoying Han
language : en
Publisher: World Scientific
Release Date : 2023-03-14
Dissipative Lattice Dynamical Systems written by Xiaoying Han and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-14 with Mathematics categories.
There is an extensive literature in the form of papers (but no books) on lattice dynamical systems. The book focuses on dissipative lattice dynamical systems and their attractors of various forms such as autonomous, nonautonomous and random. The existence of such attractors is established by showing that the corresponding dynamical system has an appropriate kind of absorbing set and is asymptotically compact in some way.There is now a very large literature on lattice dynamical systems, especially on attractors of all kinds in such systems. We cannot hope to do justice to all of them here. Instead, we have focused on key areas of representative types of lattice systems and various types of attractors. Our selection is biased by our own interests, in particular to those dealing with biological applications. One of the important results is the approximation of Heaviside switching functions in LDS by sigmoidal functions.Nevertheless, we believe that this book will provide the reader with a solid introduction to the field, its main results and the methods that are used to obtain them.
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.
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.
Attractors Under Discretisation
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Author : Xiaoying Han
language : en
Publisher: Springer
Release Date : 2017-08-11
Attractors Under Discretisation written by Xiaoying Han and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-11 with Mathematics categories.
This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained – by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size were considered, so the resulting discrete time dynamical system was also autonomous. One of the aims of this book is to present new findings on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, and in particular to examine the properties of nonautonomous omega limit sets and their approximations by numerical schemes – results that are also of importance for autonomous systems approximated by a numerical scheme with variable time steps, thus by a discrete time nonautonomous dynamical system.
Nonautonomous Bifurcation Theory
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Author : Vasso Anagnostopoulou
language : en
Publisher: Springer Nature
Release Date : 2023-05-31
Nonautonomous Bifurcation Theory written by Vasso Anagnostopoulou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-31 with Mathematics categories.
Bifurcation theory is a major topic in dynamical systems theory with profound applications. However, in contrast to autonomous dynamical systems, it is not clear what a bifurcation of a nonautonomous dynamical system actually is, and so far, various different approaches to describe qualitative changes have been suggested in the literature. The aim of this book is to provide a concise survey of the area and equip the reader with suitable tools to tackle nonautonomous problems. A review, discussion and comparison of several concepts of bifurcation is provided, and these are formulated in a unified notation and illustrated by means of comprehensible examples. Additionally, certain relevant tools needed in a corresponding analysis are presented.
The Koopman Operator In Systems And Control
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Author : Alexandre Mauroy
language : en
Publisher: Springer Nature
Release Date : 2020-02-22
The Koopman Operator In Systems And Control written by Alexandre Mauroy and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-22 with Technology & Engineering categories.
This book provides a broad overview of state-of-the-art research at the intersection of the Koopman operator theory and control theory. It also reviews novel theoretical results obtained and efficient numerical methods developed within the framework of Koopman operator theory. The contributions discuss the latest findings and techniques in several areas of control theory, including model predictive control, optimal control, observer design, systems identification and structural analysis of controlled systems, addressing both theoretical and numerical aspects and presenting open research directions, as well as detailed numerical schemes and data-driven methods. Each contribution addresses a specific problem. After a brief introduction of the Koopman operator framework, including basic notions and definitions, the book explores numerical methods, such as the dynamic mode decomposition (DMD) algorithm and Arnoldi-based methods, which are used to represent the operator in a finite-dimensional basis and to compute its spectral properties from data. The main body of the book is divided into three parts: theoretical results and numerical techniques for observer design, synthesis analysis, stability analysis, parameter estimation, and identification; data-driven techniques based on DMD, which extract the spectral properties of the Koopman operator from data for the structural analysis of controlled systems; and Koopman operator techniques with specific applications in systems and control, which range from heat transfer analysis to robot control. A useful reference resource on the Koopman operator theory for control theorists and practitioners, the book is also of interest to graduate students, researchers, and engineers looking for an introduction to a novel and comprehensive approach to systems and control, from pure theory to data-driven methods.