DISSIPATIVE LATTICE DYNAMICAL SYSTEMS

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.

Contents:
Background:Lattice Dynamical Systems: A PreviewDynamical SystemsLaplacian LDS:Lattice Laplacian ModelsApproximation of Attractors of LDSNon-Autonomous Laplacian Lattice Systems in Weighted Sequence SpacesA Selection of Lattice Models:Lattice Dynamical Systems with DelaysSet-Valued Lattice ModelsSecond Order Lattice Dynamical SystemsDiscrete Time Lattice SystemsThree Topics in BriefStochastic and Random LDS:Random Dynamical SystemsStochastic LDS with Additive NoiseStochastic LDS with Multiplicative NoiseStochastic Lattice Models with Fractional Brownian MotionsHopfield Lattice Models:Hopfield Neural Network Lattice ModelThe Hopfield Lattice Model in Weighted SpacesA Random Hopfield Lattice ModelLDS in Biology:FitzHugh-Nagumo Lattice ModelThe Amari Lattice Neural Field ModelStochastic Neural Field Models with Nonlinear NoiseLattice Systems with Switching Effects and Delayed Recovery
Readership: Researchers ranging from doctoral students to professors in mathematics and related areas. Can also be used in lecture for a graduate course.

Key Features: Readable introduction leading to actually research results Only book specifically on the topic An area of considerable current research activity Experienced authors