Dissipatve Latce Dynamical Systems

Xiaoying Han Auburn University, USA

Peter Kloeden

Universität Tübingen, Germany

Key Features

• eadable introducton leading to actuall research results

• nl book specifcall on the topic

• n area o considerable current research actvit

• E perienced authors

Descripton

There is an extensive literature in the form of papers (but no books) on latce dynamical systems. he book ocuses on dissipatve la ce d namical s stems and their a ractors o various orms such as autonomous, nonautonomous and random. he e istence o such a ractors is established b showing that the corresponding d namical s stem has an appropriate kind o absorbing set and is as mptotcall compact in some wa .

here is now a ver large literature on la ce d namical s stems, especiall on a ractors o all kinds in such s stems. We cannot hope to do ustce to all o them here. nstead, we have ocused on ke areas o representatve t pes o la ce s stems and various t pes o a ractors. ur selecton is biased b our own interests, in partcular to those dealing with biological applicatons. ne o the important results is the appro imaton o Heaviside switching unctons in L S b sigmoidal unctons.

evertheless, we believe that this book will provide the reader with a solid introducton to the feld, its main results and the methods that are used to obtain them.

Authors

Professor Xiaoying Han is Pro essor o athematcs at uburn Universit . Her main research interests are in random and nonautonomous d namical s stems and their applicatons. n additon to mathematcal anal sis o d namical s stems, she is also interested in modeling and simulaton o applied d namical s stems in biolog , chemical engineering, ecolog , material sciences, etc. She is the coauthor o the books, Applied Nonautonomous and Random Dynamical Systems (with Caraballo) and Atractors under Discretsaton (with P E Kloeden), both published b Springer rie s, as well as Random Ordinary Diferental Equatons and their Numerical Soluton (with P E Kloeden) published b Springer in 20 7.

Professor Peter E Kloeden has wide interests in the applicatons o mathematcal anal sis, numerical anal sis, stochastc anal sis and d namical s stems. He is the coauthor o several in uental books on nonautonomous d namical s stems, metric spaces o u sets, and in partcular Numerical Soluton of Stochastc Diferental Equatons (with E Platen) published b Springer in 992 and An Introducton to the Numerical Simulaton of Stochastc Diferental Equatons (with es Higham) published b S in 202 .

February 2023

Imprint: World Scientfc Publishing Compan

Extent: 380pp

Type: onograph

Series: nterdisciplinar athematcal Sciences - Volume 22

Main Subject: athematcs

Sub-Subjects: rdinar i erental E uatons Partal i erental E uatons

Probabilit heor Stochastc Processes umerical nal sis namical S stems nd Ergodic heor General pplied athematcs athematcal iolog

Keywords: La ce namical S stems Hilbert Space alued rdinar i erental E uatons eural etwork

La ce odels utonomous namical S stems onautonomous namical S stems andom namical S stems

Set alued namical S stems S stems with ela s Pullback ractors andom ractors onautonomous mega limit Sets inite dimensional ppro imatons Upper Semi Contnuous Convergence eural etworks

Readership: esearchers ranging rom doctoral students to pro essors in mathematcs and related areas. Can also be used in lecture or a graduate course

• Background:

Latce Dynamical Systems: A Preview

Dynamical Systems

• Laplacian LDS:

Laplacian Latce Models

Approximaton of Atractors LDS

Non-Autonomous Laplacian Latce Systems in Weighted Sequence Spaces

• A Selecton of Latce Models:

Latce Dynamical Systems with Delays

Set-Valued Latce Models

Second Order Latce Dynamical Systems

Discrete-Time Latce Systems

Three Topics in Brief

• Stochastc and Random LDS:

Random Dynamical Systems

Stochastc LDS with Additve Noise

Stochastc LDS with Multplicatve Noise

Stochastc Latce Models with Fractonal Brownian Motons

• Hopfeld Latce Models:

Hopfeld Neural Network Latce Model

Hopfeld Latce Model in Weighted Spaces

A Random Hopfeld Latce Model

• LDS in Biology: it hugh agumo La ce odel he mari La ce eural ield odel

Stochastc eural ield odels with onlinear oise

La ce S stems with Switching E ects and ela ed ecover