Book Review:; Dissipative Lattice Dynamical Systems

Abstract

SIAM Review, Volume 67, Issue 3, Page 655-656, August 2025.
Lattice dynamical systems (LDS) are infinite-dimensional systems of ordinary differential equations (ODEs). They can be formulated as ODEs on a Banach space of bi-infinite sequences. They may arise in various ways: some are obtained as discretizations of partial differential equations or integral equations, and others are infinite-dimensional counterparts of finite-dimensional ODE models such as the Hopfield neural network model. This book studies various kinds of LDS that might be of autonomous, nonautonomous, or random nature. It focuses on first showing that the underlying LDS induces an autonomous, nonautonomous, or random semidynamical system, then providing sufficient criteria for the existence of a global, pullback, or random attractor.