Abstract: The one - and two - dimensional numerical simulations of Duffet - Boissonade reaction-diffusion equations in pattern dynamics are performed. Setting up four kinds of different initial conditions and selecting the parameters in the equation according to Turing bifurcation condition，the hexagon pattern and fringe pattern obtained from the simulation are very similar to the experimental results.

Key words: pattern dynamics, Duffet - Boissonade reaction - diffusion equations , numerical simulation