The success of fast reaction:: A discrete reaction-diffusion model

We discuss the dynamics of a system of 2n ordinary differential equations that can be looked at as the discrete version of a system of two reaction-diffusion equations, which differ only in their sensitivity to the reaction term. Such reaction-diffusion systems Occur in evolutionary models from biology. It is known that only the fastest reacting species survives in generic situations. We prove similar results for the related discrete system and give an interpretation of the results in terms of mathematical finance.