Discrete models for the formation and evolution of spatial structure in dissipative systems

The dynamical structure of systems of coupled discrete-space, discrete-time oscillators is described. The behavior of these systems is considered for different forms of the coupling term, and parallels with cellular automaton models are pointed out. An analysis of the dynamics of dislocation structures is made and the mechanisms for their creation and destruction are discussed. Chaotic spatial patterns may arise near intermittency transitions and the mechanisms which give rise to these structures are studied. External noise can have important effects on the character of spatial patterns and their evolution; such effects are also briefly considered.