Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms

Abstract

In this chapter we discuss some real biological pattern formation problems and show how the modelling discussed earlier in the book, particularly the last chapter, can be applied. As an applications chapter of theories developed earlier, it contains considerably more biology than mathematics. Since all models for spatial pattern generation are necessarily nonlinear, practical applications require numerical solutions since no non-trivial analytical solutions are available, nor are likely to be in the near future. A preliminary linear analysis however is usually very useful, generally a necessity in fact. In each of the applications the biological modelling is discussed in detail. Most of the finite amplitude patterns reproduced are numerical solutions of the model equations and are applied directly to the specific biological situation.