Reaction–diffusion system

Reaction diffusion equations ( equations RD ) disclose processes in which a local interaction and in addition, diffusion occurs. An example from chemistry are about models for the Belousov -Zhabotinsky reaction ( BZ reaction ), resulting from the spatial pattern, because a locally oscillating chemical reaction is coupled to a diffusion process. An example from biology are spatial dispersal processes of animals and plants. Here, the interaction term often has the form of a logistics Kolmogorov equation. In RD equations are partial differential equations of second degree which are in form rate equations. So you describe the temporal change in a variable (for example, amount of substance, abundance, concentration, etc.)..

Mathematically, they have the following form:

Here are functions of time and place. They reflect the quantities whose dynamics is described. The function describes the response content. The term comes from the second Fick's law and describes the diffusion.

Reaction diffusion equations found in the field of chemistry in chemical engineering and mechanical engineering application. There are various systems are considered in which convection, diffusion and reaction occur together ( macrokinetics ). Examples are the design of chemical reactors or technical combustion processes. In developmental biology play reaction diffusion equations since Alan Turing an outstanding role in the mathematical theory of morphogenesis, see Turing mechanism. Systems with an activating and inhibiting two components play an important role in modeling the processes of structure formation localized teilchenartiger structures, so-called dissipative solitons, for example, be observed in the BZ- AOT reaction and semiconductor gas discharge systems.