Pattern Formation for a New Model of Reaction-Diffusion System

Abstract

The applications of pattern formation in nature attract a huge number of researchers and thus increase the production of researches in this field. In this paper, we introduce a new model of the reaction-diffusion system which satisfies Turing conditions and formulates complicate solutions such as pattern formation. We used for finding the numerical results and forming the patterns software COMSOL Multiphysics finite element package. We have discussed the condition of diffusion-driven instability theoretically and showed the region where these conditions can be satisfied. It was shown that the key fact for instability and the existence of pattern formation is the diffusion coefficient d. When d is large enough we can construct pattern formation with variants rings. The number of rings increases as the domain we use for study increases. Finally, we compared our results to real patterns in nature and we show how they matched together.