sentences:  Mathematically, reaction–diffusion systems take the form of semi-linear parabolic partial differential equations.They can be represented in the general form
  
  where represents the unknown vector function, is a diagonal matrix of diffusion coefficients, and accounts for all local reactions.The solutions of reaction–diffusion equations display a wide range of behaviours, including the formation of travelling waves and wave-like phenomena as well as other self-organized patterns like stripes, hexagons or more intricate structure like dissipative solitons.