Attractors Under Autonomous and Nonautonomous Perturbations
Attractors Under Autonomous and Nonautonomous Perturbations

Author: Matheus Cheque Bortolan

Publisher:

Published: 2020

Total Pages: 259

ISBN-13: 9781470456849

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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 th.

Attractors Under Autonomous and Non-autonomous Perturbations
Attractors Under Autonomous and Non-autonomous Perturbations

Author: Matheus C. Bortolan

Publisher: American Mathematical Soc.

Published: 2020-05-29

Total Pages: 246

ISBN-13: 1470453088

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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.

Attractors for infinite-dimensional non-autonomous dynamical systems
Attractors for infinite-dimensional non-autonomous dynamical systems

Author: Alexandre Carvalho

Publisher: Springer Science & Business Media

Published: 2012-09-25

Total Pages: 434

ISBN-13: 1461445817

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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 for infinite-dimensional non-autonomous dynamical systems
Attractors for infinite-dimensional non-autonomous dynamical systems

Author: Alexandre Carvalho

Publisher: Springer

Published: 2012-09-25

Total Pages: 412

ISBN-13: 9781461445814

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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 for infinite-dimensional non-autonomous dynamical systems
Attractors for infinite-dimensional non-autonomous dynamical systems

Author: Alexandre Carvalho

Publisher: Springer Science & Business Media

Published: 2012-09-26

Total Pages: 434

ISBN-13: 1461445809

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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.

Global Attractors of Non-autonomous Dissipative Dynamical Systems
Global Attractors of Non-autonomous Dissipative Dynamical Systems

Author: David N. Cheban

Publisher: World Scientific

Published: 2004

Total Pages: 524

ISBN-13: 9812563083

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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.

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

Author: David N Cheban

Publisher: World Scientific

Published: 2014-12-15

Total Pages: 616

ISBN-13: 9814619841

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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.

Global Attractors Of Nonautonomous Dissipative Dynamical Systems
Global Attractors Of Nonautonomous Dissipative Dynamical Systems

Author: David N Cheban

Publisher: World Scientific

Published: 2004-11-29

Total Pages: 524

ISBN-13: 9814481866

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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.

Nonautonomous Bifurcation Theory
Nonautonomous Bifurcation Theory

Author: Vasso Anagnostopoulou

Publisher: Springer Nature

Published: 2023-05-31

Total Pages: 159

ISBN-13: 303129842X

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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.

Local Attractor Continuation of Non-autonomously Perturbed Systems
Local Attractor Continuation of Non-autonomously Perturbed Systems

Author: Martin Kell

Publisher:

Published: 2011

Total Pages:

ISBN-13:

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Using Conley theory we show that local attractors remain (past) attractors under small non-autonomous perturbations. In particular, the attractors of the perturbed systems will have positive invariant neighborhoods and converge upper semicontinuously to the original attractor. The result is split into a finite-dimensional part (locally compact) and an infinite-dimensional part (not necessarily locally compact). The finite-dimensional part will be applicable to bounded random noise, i.e. continuous time random dynamical systems on a locally compact metric space which are uniformly close the unperturbed deterministic system. The closenessʺ will be defined via a (simpler version of) convergence coming from singular perturbations theory.