I have stumbled upon a very basic question on Reaction Diffusion Modelling and Pattern Formation. My question is;
Can we define some kind of general form(s) of Reaction Terms in R&D Equation so that we can find the various patterns? Or, is it possible to know in prior for what types of Reaction Terms in R&D Equation, we can find the various patterns? Is it possible to put it in some general form(s)?
In principle, we cannot define any particular form of the reaction terms in RD equations. There is no universal form of the reaction terms where one can surely say - yes, these will lead to patter formation. Each case is special. However, one thing is clear - these terms have to be nonlinear. Otherwise one will not get pattern formation.
Alan Turing proposed a very important idea why pattern formation can take place in RD systems. Namely, systems with nonlinear reactions that are locally stable should become unstable in the presence of diffusion.
You could also have a look at a particular case of the FitzHugh–Nagumo model: http://en.wikipedia.org/wiki/FitzHugh%E2%80%93Nagumo_model
- Badges
- Science topic
- Similar topics
- Engineering
- Modeling