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Nonautonomous Dynamics
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Book Synopsis Nonautonomous Dynamics by : David N. Cheban
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).
Book Synopsis Nonautonomous Dynamical Systems by : Peter E. Kloeden
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.
Book Synopsis Nonautonomous Dynamical Systems in the Life Sciences by : Peter E. Kloeden
Download or read book Nonautonomous Dynamical Systems in the Life Sciences written by Peter E. Kloeden and published by Springer. This book was released on 2014-01-22 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Applied Nonautonomous and Random Dynamical Systems by : Tomás Caraballo
Download or read book Applied Nonautonomous and Random Dynamical Systems written by Tomás Caraballo and published by Springer. This book was released on 2017-01-31 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 and published by World Scientific. This book was released on 2004-11-29 with total page 528 pages. 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.
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 and published by World Scientific. This book was released on 2020-11-25 with total page 157 pages. 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.
Book Synopsis Attractivity and Bifurcation for Nonautonomous Dynamical Systems by : Martin Rasmussen
Download or read book Attractivity and Bifurcation for Nonautonomous Dynamical Systems written by Martin Rasmussen and published by Springer. This book was released on 2007-05-26 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions.
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 and published by World Scientific. This book was released on 2004 with total page 524 pages. 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
Book Synopsis Model Emergent Dynamics in Complex Systems by : A. J. Roberts
Download or read book Model Emergent Dynamics in Complex Systems written by A. J. Roberts and published by SIAM. This book was released on 2014-12-18 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arising out of the growing interest in and applications of modern dynamical systems theory, this book explores how to derive relatively simple dynamical equations that model complex physical interactions. The author’s objectives are to use sound theory to explore algebraic techniques, develop interesting applications, and discover general modeling principles. Model Emergent Dynamics in Complex Systems unifies into one powerful and coherent approach the many varied extant methods for mathematical model reduction and approximation. Using mathematical models at various levels of resolution and complexity, the book establishes the relationships between such multiscale models and clarifying difficulties and apparent paradoxes and addresses model reduction for systems, resolves initial conditions, and illuminates control and uncertainty. The basis for the author’s methodology is the theory and the geometric picture of both coordinate transforms and invariant manifolds in dynamical systems; in particular, center and slow manifolds are heavily used. The wonderful aspect of this approach is the range of geometric interpretations of the modeling process that it produces—simple geometric pictures inspire sound methods of analysis and construction. Further, pictures drawn of state spaces also provide a route to better assess a model’s limitations and strengths. Geometry and algebra form a powerful partnership and coordinate transforms and manifolds provide a powerfully enhanced and unified view of a swathe of other complex system modeling methodologies such as averaging, homogenization, multiple scales, singular perturbations, two timing, and WKB theory. Audience Advanced undergraduate and graduate students, engineers, scientists, and other researchers who need to understand systems and modeling at different levels of resolution and complexity will all find this book useful.
Book Synopsis Global Attractors Of Non-autonomous Dynamical And Control Systems (2nd Edition) by : Cheban David N
Download or read book Global Attractors Of Non-autonomous Dynamical And Control Systems (2nd Edition) written by Cheban David N and published by World Scientific. This book was released on 2014-12-15 with total page 616 pages. 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.
Book Synopsis Attractors for infinite-dimensional non-autonomous dynamical systems by : Alexandre Carvalho
Download or read book Attractors for infinite-dimensional non-autonomous dynamical systems written by Alexandre Carvalho and published by Springer Science & Business Media. This book was released on 2012-09-26 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book treats the theory of attractors for non-autonomous dynamical systems. The aim of the book is to give a coherent account of the current state of the theory, using the framework of processes to impose the minimum of restrictions on the nature of the non-autonomous dependence. The book is intended as an up-to-date summary of the field, but much of it will be accessible to beginning graduate students. Clear indications will be given as to which material is fundamental and which is more advanced, so that those new to the area can quickly obtain an overview, while those already involved can pursue the topics we cover more deeply.
Book Synopsis Dynamical Chaos by : Vadim Semenovich Anishchenko
Download or read book Dynamical Chaos written by Vadim Semenovich Anishchenko and published by World Scientific. This book was released on 1995 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, bifurcational mechanisms of the development, structure and properties of chaotic attractors are investigated by numerical and physical experiments based on the methods of the modern theory of nonlinear oscillations. The typical bifurcations of regular and chaotic attractors which are due to parameter variations are analyzed.Regularities of the transition to chaos via the collapse of quasiperiodic oscillations with two and three frequencies are investigated in detail. The book deals with the problems of chaotic synchronization, interaction of attractors and the phenomenon of stochastic resonance. The problems of fluctuation influence on the bifurcations and properties of chaotic attractors are investigated more closely.All principal problems are investigated by the comparison of theoretical and numerical results and data from physical experiments.
Book Synopsis The Cambridge Handbook of Artificial Intelligence by : Keith Frankish
Download or read book The Cambridge Handbook of Artificial Intelligence written by Keith Frankish and published by Cambridge University Press. This book was released on 2014-06-12 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Artificial intelligence, or AI, is a cross-disciplinary approach to understanding, modeling, and creating intelligence of various forms. It is a critical branch of cognitive science, and its influence is increasingly being felt in other areas, including the humanities. AI applications are transforming the way we interact with each other and with our environment, and work in artificially modeling intelligence is offering new insights into the human mind and revealing new forms mentality can take. This volume of original essays presents the state of the art in AI, surveying the foundations of the discipline, major theories of mental architecture, the principal areas of research, and extensions of AI such as artificial life. With a focus on theory rather than technical and applied issues, the volume will be valuable not only to people working in AI, but also to those in other disciplines wanting an authoritative and up-to-date introduction to the field.
Book Synopsis Control Theory for Physicists by : John Bechhoefer
Download or read book Control Theory for Physicists written by John Bechhoefer and published by Cambridge University Press. This book was released on 2021-04-01 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control theory, an interdisciplinary concept dealing with the behaviour of dynamical systems, is an important but often overlooked aspect of physics. This is the first broad and complete treatment of the topic tailored for physicists, one which goes from the basics right through to the most recent advances. Simple examples develop a deep understanding and intuition for the systematic principles of control theory, beyond the recipes given in standard engineering-focused texts. Up-to-date coverage of control of networks and complex systems, and a thorough discussion of the fundamental limits of control, including the limitations placed by causality, information theory, and thermodynamics are included. In addition it explores important recent advances in stochastic thermodynamics on the thermodynamic costs of information processing and control. For all students of physics interested in control theory, this classroom-tested, comprehensive approach to the topic with online solutions and further materials delivers both fundamental principles and current developments.
Book Synopsis Tackling the Inverse Problem for Non-Autonomous Systems by : Tomislav Stankovski
Download or read book Tackling the Inverse Problem for Non-Autonomous Systems written by Tomislav Stankovski and published by Springer Science & Business Media. This book was released on 2013-08-27 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents a new method for following evolving interactions between coupled oscillatory systems of the kind that abound in nature. Examples range from the subcellular level, to ecosystems, through climate dynamics, to the movements of planets and stars. Such systems mutually interact, adjusting their internal clocks, and may correspondingly move between synchronized and non-synchronized states. The thesis describes a way of using Bayesian inference to exploit the presence of random fluctuations, thus analyzing these processes in unprecedented detail. It first develops the basic theory of interacting oscillators whose frequencies are non-constant, and then applies it to the human heart and lungs as an example. Their coupling function can be used to follow with great precision the transitions into and out of synchronization. The method described has the potential to illuminate the ageing process as well as to improve diagnostics in cardiology, anesthesiology and neuroscience, and yields insights into a wide diversity of natural processes.
Author :Sergey N. Vladimirov Publisher :Scientific Research Publishing, Inc. USA ISBN 13 :1618960563 Total Pages :240 pages Book Rating :4.6/5 (189 download)
Book Synopsis Non-traditional Dynamics in Electronics: Theory and Practice by : Sergey N. Vladimirov
Download or read book Non-traditional Dynamics in Electronics: Theory and Practice written by Sergey N. Vladimirov and published by Scientific Research Publishing, Inc. USA. This book was released on 2010-10-04 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of the proposed book is devoted to investigation of non-trivial problems of functioning of Ultra-High-Frequency (UHF) electronic devices and systems in the various type dynamic instability modes. Both flows and maps (representations) are considered because the relation between maps and flows was repeatedly discussed in different publications. On the contrary, all systems described in the offered book for the first time are considered from the point of view either internal structure, or the description and analysis.
Book Synopsis Dynamics and Bifurcations of Non-Smooth Mechanical Systems by : Remco I. Leine
Download or read book Dynamics and Bifurcations of Non-Smooth Mechanical Systems written by Remco I. Leine and published by Springer Science & Business Media. This book was released on 2013-03-19 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.
