Attractors Under Discretisation

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Attractors Under Discretisation

Author : Xiaoying Han
Publisher : Springer
ISBN 13 : 3319619349
Total Pages : 122 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Attractors Under Discretisation by : Xiaoying Han

Download or read book Attractors Under Discretisation written by Xiaoying Han and published by Springer. This book was released on 2017-08-11 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Attractors for infinite-dimensional non-autonomous dynamical systems

Author : Alexandre Carvalho
Publisher : Springer Science & Business Media
ISBN 13 : 1461445809
Total Pages : 434 pages
Book Rating : 4.4/5 (614 download)

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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.

Attractors, Shadowing, And Approximation Of Abstract Semilinear Differential Equations

Author : Sergey I Piskarev
Publisher : World Scientific
ISBN 13 : 9811272794
Total Pages : 213 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Attractors, Shadowing, And Approximation Of Abstract Semilinear Differential Equations by : Sergey I Piskarev

Download or read book Attractors, Shadowing, And Approximation Of Abstract Semilinear Differential Equations written by Sergey I Piskarev and published by World Scientific. This book was released on 2023-07-05 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to some branches of the theory of approximation of abstract differential equations, namely, approximation of attractors in the case of hyperbolic equilibrium points, shadowing, and approximation of time-fractional semilinear problems.In this book, the most famous methods of several urgent branches of the theory of abstract differential equations scattered in numerous journal publications are systematized and collected together, which makes it convenient for the initial study of the subject and also for its use as a reference book. The presentation of the material is closed and accompanied by examples; this makes it easier to understand the material and helps beginners to quickly enter into the circle of ideas discussed.The book can be useful for specialists in partial differential equations, functional analysis, theory of approximation of differential equations, and for all researchers, students, and postgraduates who apply these branches of mathematics in their work.

Random Ordinary Differential Equations and Their Numerical Solution

Author : Xiaoying Han
Publisher : Springer
ISBN 13 : 981106265X
Total Pages : 250 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Random Ordinary Differential Equations and Their Numerical Solution by : Xiaoying Han

Download or read book Random Ordinary Differential Equations and Their Numerical Solution written by Xiaoying Han and published by Springer. This book was released on 2017-10-25 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs). RODEs are used in many important applications and play a fundamental role in the theory of random dynamical systems. They can be analyzed pathwise with deterministic calculus, but require further treatment beyond that of classical ODE theory due to the lack of smoothness in their time variable. Although classical numerical schemes for ODEs can be used pathwise for RODEs, they rarely attain their traditional order since the solutions of RODEs do not have sufficient smoothness to have Taylor expansions in the usual sense. However, Taylor-like expansions can be derived for RODEs using an iterated application of the appropriate chain rule in integral form, and represent the starting point for the systematic derivation of consistent higher order numerical schemes for RODEs. The book is directed at a wide range of readers in applied and computational mathematics and related areas as well as readers who are interested in the applications of mathematical models involving random effects, in particular in the biological sciences.The level of this book is suitable for graduate students in applied mathematics and related areas, computational sciences and systems biology. A basic knowledge of ordinary differential equations and numerical analysis is required.

The Structure of Attractors in Dynamical Systems

Author : N.G. Markley
Publisher : Springer
ISBN 13 : 3540357513
Total Pages : 275 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis The Structure of Attractors in Dynamical Systems by : N.G. Markley

Download or read book The Structure of Attractors in Dynamical Systems written by N.G. Markley and published by Springer. This book was released on 2007-01-05 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Continuation and Bifurcations: Numerical Techniques and Applications

Author : Dirk Roose
Publisher : Springer Science & Business Media
ISBN 13 : 9400906595
Total Pages : 415 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Continuation and Bifurcations: Numerical Techniques and Applications by : Dirk Roose

Download or read book Continuation and Bifurcations: Numerical Techniques and Applications written by Dirk Roose and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Research Workshop, Leuven, Belgium, September 18-22, 1989

Dynamical Systems and Numerical Analysis

Author : Andrew Stuart
Publisher : Cambridge University Press
ISBN 13 : 9780521645638
Total Pages : 708 pages
Book Rating : 4.6/5 (456 download)

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Book Synopsis Dynamical Systems and Numerical Analysis by : Andrew Stuart

Download or read book Dynamical Systems and Numerical Analysis written by Andrew Stuart and published by Cambridge University Press. This book was released on 1998-11-28 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulated as dynamical systems and the convergence and stability properties of the methods are examined.

Global Attractors Of Nonautonomous Dissipative Dynamical Systems

Author : David N Cheban
Publisher : World Scientific
ISBN 13 : 9814481866
Total Pages : 528 pages
Book Rating : 4.8/5 (144 download)

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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.

Global Attractors of Non-autonomous Dissipative Dynamical Systems

Author : David N. Cheban
Publisher : World Scientific
ISBN 13 : 9812563083
Total Pages : 524 pages
Book Rating : 4.8/5 (125 download)

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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 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.

Nonautonomous Dynamical Systems

Author : Peter E. Kloeden
Publisher : American Mathematical Soc.
ISBN 13 : 0821868713
Total Pages : 274 pages
Book Rating : 4.8/5 (218 download)

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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.

Global Attractors Of Non-autonomous Dynamical And Control Systems (2nd Edition)

Author : Cheban David N
Publisher : World Scientific
ISBN 13 : 9814619841
Total Pages : 616 pages
Book Rating : 4.8/5 (146 download)

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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.

Geometric Theory of Discrete Nonautonomous Dynamical Systems

Author : Christian Pötzsche
Publisher : Springer
ISBN 13 : 3642142583
Total Pages : 399 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Geometric Theory of Discrete Nonautonomous Dynamical Systems by : Christian Pötzsche

Download or read book Geometric Theory of Discrete Nonautonomous Dynamical Systems written by Christian Pötzsche and published by Springer. This book was released on 2010-08-24 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonautonomous dynamical systems provide a mathematical framework for temporally changing phenomena, where the law of evolution varies in time due to seasonal, modulation, controlling or even random effects. Our goal is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes). These dynamical systems are generated by implicit difference equations, which explicitly depend on time. Compactness and dissipativity conditions are provided for such problems in order to have attractors using the natural concept of pullback convergence. Concerning a necessary linear theory, our hyperbolicity concept is based on exponential dichotomies and splittings. This concept is in turn used to construct nonautonomous invariant manifolds, so-called fiber bundles, and deduce linearization theorems. The results are illustrated using temporal and full discretizations of evolutionary differential equations.

Modeling, Stochastic Control, Optimization, and Applications

Author : George Yin
Publisher : Springer
ISBN 13 : 3030254984
Total Pages : 599 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Modeling, Stochastic Control, Optimization, and Applications by : George Yin

Download or read book Modeling, Stochastic Control, Optimization, and Applications written by George Yin and published by Springer. This book was released on 2019-07-16 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.

Advances in Discrete Dynamical Systems, Difference Equations and Applications

Author : Saber Elaydi
Publisher : Springer Nature
ISBN 13 : 303125225X
Total Pages : 534 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Advances in Discrete Dynamical Systems, Difference Equations and Applications by : Saber Elaydi

Download or read book Advances in Discrete Dynamical Systems, Difference Equations and Applications written by Saber Elaydi and published by Springer Nature. This book was released on 2023-03-25 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises selected papers of the 26th International Conference on Difference Equations and Applications, ICDEA 2021, held virtually at the University of Sarajevo, Bosnia and Herzegovina, in July 2021. The book includes the latest and significant research and achievements in difference equations, discrete dynamical systems, and their applications in various scientific disciplines. The book is interesting for Ph.D. students and researchers who want to keep up to date with the latest research, developments, and achievements in difference equations, discrete dynamical systems, and their applications, the real-world problems.

Attractors and Methods

Author : Boling Guo
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110587262
Total Pages : 413 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Attractors and Methods by : Boling Guo

Download or read book Attractors and Methods written by Boling Guo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-07-09 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the fi rst volume is on the existence and properties for attractors and inertial manifolds. This volume highlights the use of modern analytical tools and methods such as the geometric measure method, center manifold theory in infinite dimensions, the Melnihov method, spectral analysis and so on for infinite-dimensional dynamical systems. The second volume includes the properties of global attractors, the calculation of discrete attractors, structures of small dissipative dynamical systems, and the existence and stability of solitary waves. Contents Discrete attractor and approximate calculation Some properties of global attractor Structures of small dissipative dynamical systems Existence and stability of solitary waves

Differential Equations

Author : C. M. Dafermos
Publisher : CRC Press
ISBN 13 : 100010415X
Total Pages : 811 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Differential Equations by : C. M. Dafermos

Download or read book Differential Equations written by C. M. Dafermos and published by CRC Press. This book was released on 2020-08-26 with total page 811 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an outcome of the EQUADIFF 87 conference in Greece. It addresses a wide spectrum of topics in the theory and applications of differential equations, ordinary, partial, and functional. The book is intended for mathematics and scientists.

Dissipative Lattice Dynamical Systems

Author : Xiaoying Han
Publisher : World Scientific
ISBN 13 : 9811267774
Total Pages : 381 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Dissipative Lattice Dynamical Systems by : Xiaoying Han

Download or read book Dissipative Lattice Dynamical Systems written by Xiaoying Han and published by World Scientific. This book was released on 2023-03-14 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.