Dissipative Lattice Dynamical Systems: 22 (Interdisciplinary Mathematical Sciences) - Hardcover

Xiaoying Han; Peter Kloeden

Hardcover

ISBN 10: 9811267758 ISBN 13: 9789811267758

Publisher: World Scientific Publishing Co Pte Ltd, 2023

Synopsis

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.

About this title

About the Author

Professor Xiaoying Han is Professor of Mathematics at Auburn University. Her main research interests are in random and nonautonomous dynamical systems and their applications. In addition to mathematical analysis of dynamical systems, she is also interested in modeling and simulation of applied dynamical systems in biology, chemical engineering, ecology, material sciences, etc. She is the coauthor of the books, Applied Nonautonomous and Random Dynamical Systems (with T Caraballo) and Attractors under Discretisation (with P E Kloeden), both published by SpringerBriefs, as well as Random Ordinary Differential Equations and their Numerical Solution (with P E Kloeden) published by Springer in 2017.

Professor Peter E Kloeden has wide interests in the applications of mathematical analysis, numerical analysis, stochastic analysis and dynamical systems. He is the coauthor of several influential books on nonautonomous dynamical systems, metric spaces of fuzzy sets, and in particular Numerical Solution of Stochastic Differential Equations (with E Platen) published by Springer in 1992 and An Introduction to the Numerical Simulation of Stochastic Differential Equations (with Des Higham) published by SIAM in 2021.

Professor Kloeden is a Fellow of the Society of Industrial and Applied Mathematics and was awarded the W T & Idalia Reid Prize from Society of Applied and Industrial Mathematics in 2006. He is the retired Professor of Applied and Instrumental Mathematics at the Goethe University in Frankfurt am Main and is currently a visiting researcher at the Universität Tübingen and an Affiliated Professor at Auburn University. His current interests focus on nonautonomous and random dynamical systems and their applications in the biological sciences.

Edition details

• Publisher: World Scientific Publishing Co Pte Ltd
• Publication date: 2023
• Language: English
• ISBN 10: 9811267758
• ISBN 13: 9789811267758
• Binding: Hardcover
• Number of pages: 380