In this work, we analyse a pair of two-dimensional coupled reaction-diusion equations known as the Gray-Scott model, in which spot patterns have been observed. We focus on stationary patterns, and begin by deriving the asymptotic scaling of the parameters and variables necessary for the analysis of these patterns. A complete bifurcation study of these solutions is presented. The main mathematic...

Nowadays, an abundance of sensors are used to collect very large datasets containing spatial points which can be mined and analyzed to extract meaningful patterns and information. This article examines patterns which describe the dispersion of 2D data around a central tendency. Several state of the art patterns for point cluster analysis are presented and critiqued before a new pattern, the Ori...

Spatial distributions of biological species are an important source of information for understanding local interactions at the scale of individuals. Technological advances have made it easier to measure these distributions as spatial point patterns, specifying the locations of individuals. Extensive attention has been devoted to analyzing the second-order structure of such point patterns by foc...