Abstract
We discuss a variety of experimental and theoretical studies of localized stationary spots, oscillons, and localized oscillatory clusters, moving and breathing spots, and localized waves in reaction-diffusion systems. We also suggest some promising directions for future research in this area.
A localized pattern consists of one or more regions in one state, typically characterized by a set of concentrations, temperature, and/or other variables, surrounded by a region in a qualitatively different state. Such patterns may be stationary or oscillatory, static or moving. They may have potential applications in biological morphogenesis and in technology. For example, blood clotting can be considered as the formation of localized patterns.1,2 Some neurological disorders, such as epilepsy, are characterized by spatially localized oscillations in the brain.3 Localized stationary spots have been suggested as components for structureless memory devices.4–9 Specific interactions between stationary localized spots or oscillons10 (objects that are stationary in space and oscillatory in time) or between moving localized spots11,12 in reaction-diffusion systems may provide a basis for future chemical processors in two dimensions (2D) and even in 3D. Here, we present an overview of the wealth of localized patterns that have been observed experimentally in reaction-diffusion systems and give a brief survey of approaches to modeling these phenomena.