Applied Nonautonomous and Random Dynamical Systems

Applied Dynamical Systems

verfasst von: Tomás Caraballo, Xiaoying Han

Verlag: Springer International Publishing

Buchreihe : SpringerBriefs in Mathematics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

The research on the theories of dynamical systems (autonomous, nonautonomous or stochastic) has been receiving much attention over the last decades, due to the fact that many real world phenomena can be modeled by a system of differential or difference equations which generates one dynamical system. A general theory for dynamical systems allows us to analyze various type of evolutionary problems, but is sometimes over abstract for practitioner research. In particular, while analyzing finite dimensional systems, the theory required may be less complicated and more intuitive than the general theory for abstract dynamical systems. In this book, we will set up a unified framework of dynamical systems accessible to researchers with different background, which suffices to analyze finite dimensional systems arising in applied sciences and engineering.

Tomás Caraballo, Xiaoying Han

Chapter 2. Autonomous Dynamical Systems

Abstract

The theory of autonomous dynamical systems is now well established after being studied intensively over the past years. In this chapter we will provide a brief review of autonomous dynamical systems, as the background and motivation to introduce nonautonomous and random dynamical systems which are the major topics of the book.

Tomás Caraballo, Xiaoying Han

Chapter 3. Nonautonomous Dynamical Systems

Abstract

It was emphasized in Chap. 2 that the formulation of an autonomous dynamical system as a group (or semigroup) of mappings is based on the fact that such systems depend only on the elapsed time \(t - t_0\) instead of the starting time \(t_0\) or current time t independently.

Tomás Caraballo, Xiaoying Han

Chapter 4. Random Dynamical Systems

Abstract

In this chapter we will introduce methods and techniques to analyze models with stochasticity or randomness. In particular we will establish the framework of random dynamical systems and introduce the concept of random attractors.

Tomás Caraballo, Xiaoying Han

Backmatter

Titel: Applied Nonautonomous and Random Dynamical Systems
verfasst von: Tomás Caraballo
Xiaoying Han
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-49247-6
Print ISBN: 978-3-319-49246-9
DOI: https://doi.org/10.1007/978-3-319-49247-6