Attractors Under Discretisation PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Attractors Under Discretisation PDF full book. Access full book title Attractors Under Discretisation by Xiaoying Han. Download full books in PDF and EPUB format.
Author: Xiaoying Han
Publisher: Springer
ISBN: 3319619349
Category : Mathematics
Languages : en
Pages : 121
Get Book Here
Book Description
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.
Author: Xiaoying Han
Publisher: Springer
ISBN: 3319619349
Category : Mathematics
Languages : en
Pages : 121
Get Book Here
Book Description
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.
Author: N.G. Markley
Publisher: Springer
ISBN: 3540357513
Category : Mathematics
Languages : en
Pages : 275
Get Book Here
Book Description
Author: Lars Grüne
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
Book Description
Author: Lars Grüne
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
Book Description
Author: David N. Cheban
Publisher: World Scientific
ISBN: 9812560289
Category : Mathematics
Languages : en
Pages : 524
Get Book Here
Book Description
- The book is intended to the experts in qualitative theory of differential equations, dynamical systems and their applications
Author: Christian Pötzsche
Publisher: Springer Science & Business Media
ISBN: 3642142575
Category : Mathematics
Languages : en
Pages : 422
Get Book Here
Book Description
The goal of this book 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).
Author: Dirk Roose
Publisher: Springer Science & Business Media
ISBN: 9400906595
Category : Mathematics
Languages : en
Pages : 415
Get Book Here
Book Description
Proceedings of the NATO Advanced Research Workshop, Leuven, Belgium, September 18-22, 1989
Author: David N Cheban
Publisher: World Scientific
ISBN: 9814619841
Category : Mathematics
Languages : en
Pages : 616
Get Book Here
Book Description
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: David N Cheban
Publisher: World Scientific
ISBN: 9814481866
Category : Mathematics
Languages : en
Pages : 524
Get Book Here
Book Description
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.
Author: Xiaoying Han
Publisher: Springer
ISBN: 981106265X
Category : Mathematics
Languages : en
Pages : 252
Get Book Here
Book Description
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.
