In recent years there has been growing interest in the study of the nonlinear spatio-temporal dynamics of problems appearing in various ?elds of science and engineering. In a wide class of such systems an important place is - cupied by active lattice dynamical systems. Active lattice systems are, e. g. , networks of identical or almost identical interacting units ordered in space. The activity of lattices is provided by the activity of units in them that possess energy or matter sources. In real (1D, 2D or 3D) space, processes develop by means of various types of connections, the simplest being di?usion. The uniqueness of lattice systems is that they represent spatially extended systems while having a ?nite-dimensional phase space. Therefore, active lattice s- tems are of interest for the study of multidimensional dynamical systems and the theory of nonlinear waves and dissipative structures of extended systems as well. The theory of nonlinear waves and dissipative structures of spatially distributed systems demands using theoretical methods and approaches of the qualitative theory of dynamical systems, bifurcation theory, and numerical methods or computer experiments. In other words, the investigation of spat- temporal dynamics in active lattice systems demands a multitool, synergetic approach, which we shall use in this book.
Rezensionen / Stimmen
"The book may serve as an invaluable guide to all those interested in the rich phenomenology of spatio-temporal dynamic phenomena in active lattices, providing the reader with a variety of analytical and numerical methods that can be used in the study of concrete applications. In sum, it is a highly enjoyable, well-written book by two leading scientists in the field, with carefully chosen material, which is highly recommended to anyone wanting a good introduction to the subject." (Mathematical Reviews 2003b)
"In an applied, descriptive manner, the authors present and corroborate results through a mixture of heuristics, numerical investigations and mathematical analysis guided by general methods from geometric dynamical systems theory. [...] Each of the well written chapters starts with a motivation and ends with a summary; general conclusions and perspectives are given in the final chapter. [...] This book provides an easily accessible introduction and overview of phenomena and the current state of understanding in the field of waves and synchronization in spatially discrete systems." (Zentralblatt MATH, 1006, 2003)
"This book gives a comprehensive account of synergetic phenomena in active lattices. . throughout the book insights on the possible use of the results in applications such as computer architecture or neuronal science are given. . The book may serve as an invaluable guide to all those interested in the rich pheonomenology of spatio-temporal dynamic phenomena in active lattices . . In sum, it is a highly enjoyable, well-written book . which is highly recommended to anyone wanting a good introduction to the subject." (Athanasios Yannacopoulos, Mathematical Reviews, Issue 2003 b)
"The present textbook concerns pattern formation in lattices of coupled cells with oscillatory or excitable dynamics. In an applied, descriptive manner, the authors present and corroborate results through a mixture of heuristics, numericalinvestigations and mathematical analysis guided by general methods from geometric dynamical systems theory. . This book provides an easily accessible introduction and overview of phenomena and the current state of understanding in the field of waves and synchronization in spatially discrete systems." (Jens Rademacher, Zentralblatt MATH, Vol. 1006, 2003)
