Synergetic Phenomena in Active Lattices : Patterns

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.