Pattern selection of three components Gray-Scott model

Abstract

Abstract The reaction-diffusion system demonstrates a variety of dynamical behaviours, and has become a standard model for explaining complex Turing patterns. In this work we have performed the analytical analysis of the three components Gray-Scott reaction-diffusion system. The analytical conditions for Turing instability about the homogeneous steady state has been derived. The linear stability is theoretically discussed. To determine the nature of pattern amplitude equation is derived by using weakly nonlinear analysis, which enumerates about the rich dynamical behaviour of this model, e.g. spot-, strip- and hexagon-patterns.