Local activity in reaction-diffusion equations and pattern formation

This paper deals with pattern formation in various models described by reaction-diffusion equations. Different spatio-temporal patterns can emerge depending on the kinetics in these models. There are turbulent double rotating spirals, cellular, and target patterns. Reactions are represented by composition changes with a particular probability of grid positions, depending on the occupation of neighboring grid positions. In these cases, pattern formation is self-organized in the oscillatory medium of catalytic oscillators. Self-organizing patterns will only occur in specific reaction condition regimes. An application in nano-structures will be presented.