PATTERN FORMATION IN NOISY SELF-REPLICATING SPOTS

Abstract

Among reaction–diffusion systems showing Turing patterns, the diffusive Gray–Scott model [Pearson, 1993], stands out by showing self-replicating patterns (spots), which makes it the ideal simple model for developmental research. A first study of the influence of noise in the Gray–Scott model was performed by Lesmes et al. [2003] concluding that there exists an optimal noise intensity for which spot multiplication is maximal. Here we show in detail the transition from nonspotlike to spotlike pattern, with the identification of a wide range of noise intensities instead of an optimal value for which this transition occurs. Additional studies also reveal that noise produces a shift and a shrinkage of the regions of spatial patterns in the parameters space, without introducing qualitative changes to the diagram.