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Applied Nonautonomous and Random Dynamical Systems

Applied Dynamical Systems

  • Book
  • © 2016

Overview

Authors:
  1. Tomás Caraballo

    1. Facultad de Matematicas, Universidad de Sevilla, Sevilla, Spain

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    You can also search for this author in PubMed   Google Scholar

  2. Xiaoying Han

    1. Department of Mathematics and Statistics, Auburn University, Auburn, USA

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    You can also search for this author in PubMed   Google Scholar

  • Intended for mathematicians, as well as to researchers from the applied sciences
  • A self-contained book that includes related materials
  • Presents in detail how the theory of pullback attractors and random attractors is employed in biological applications
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Tomás Caraballo, Xiaoying Han
    Pages 1-9

  3. Autonomous Dynamical Systems

    • Tomás Caraballo, Xiaoying Han
    Pages 11-33

  4. Nonautonomous Dynamical Systems

    • Tomás Caraballo, Xiaoying Han
    Pages 35-66

  5. Random Dynamical Systems

    • Tomás Caraballo, Xiaoying Han
    Pages 67-104

  6. Back Matter

    Pages 105-108
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Keywords

About this book

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 thecoverage.

Reviews

“This brief monograph gives an introduction to the theory of non-autonomous, random and  stochastic dynamical systems. The book is accessible for a wide audience and gives some citations to more recent research. ... The main emphasis is on the study of the long-term behavior of solutions and pullback attractors. A discussion of future research directions supplements the topics presented.” (Henri Schurz, Mathematical Reviews, June, 2017)

Authors and Affiliations

  • Facultad de Matematicas, Universidad de Sevilla, Sevilla, Spain

    Tomás Caraballo

  • Department of Mathematics and Statistics, Auburn University, Auburn, USA

    Xiaoying Han

About the authors

Tomás Caraballo graduated with a degree in Mathematical Sciences in 1984, and received his Ph.D.  in the same subject at the Universidad de Sevilla (Spain) in 1988. He is currently a Catedrático de Universidad (Full Professor) at the Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla. He has participated in or been Principal Investigator for more than 20 research projects. He has authored or co-authored more than 180 papers, has supervised 10 doctoral theses, and has been associate or guest editor of numerous scientific journals. His current research interests are non-autonomous and random dynamical systems, both in finite and infinite dimensions, stochastic ordinary and partial differential equations with memory, delay, impulses and their applications to real models from the applied sciences.

Xiaoying Han received her Ph.D. in mathematics from the State University of New York at Buffalo in 2007. She is an associate professor of mathematics at Auburn University’s Department of Mathematics and Statistics, Alabama, USA. Her main research focuses are nonautonomous and random dynamical systems and their applications, and she is also interested in modeling, analysis and simulation of stochastic systems arising in applied sciences and engineering.

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