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.
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