Spatiotemproal pattern formation in a reaction-diffusion system

Spatiotemporal pattern formations are often found in reaction-diffusion systems. One-dimension patterns have been obtained in the extended Brusselator model. In this paper, linear stability analysis is applied to the Brusselator model, a series of time-space pattern are obtained in two-dimension space by numerical simulations. Homogeneous bulk oscillations are unstable when systems are far away bifurcation point. We explain that some patterns are formed because of instabilities and interaction between instabilities. We further point out that the Brusselator model is a perfect model unraveling dissipative structure and the mechanism of patterns.