Dynamics and spatial organization in two-species competition

Le résumé fourni par la source

The authors investigate the time evolution of a prototypical population biology reaction which involves reproduction, self-regulation and competitive annihilation of two distinct species. In one dimension, the authors use a quasistatic analysis to argue that for a system with equal initial densities of two strongly competing species, an alternating pattern of domains forms whose lengths grow logarithmically with time. A scaling analysis of the underlying master equation, as well as numerical integration of the reaction diffusion equations support this result. For unequal initial densities, the concentration of the minority species undergoes a power-law decay with a non-universal exponent. The authors generalize the model by allowing for a nonlinear self-regulation term in the rate equations. As a function of the exponent of this nonlinearity, the typical domain size may grow either as a power law with time or saturate at a finite value. This general approach also suggests that a coarsening domain mosaic occurs in arbitrary spatial dimensions. In two dimensions, numerical integration of the reaction diffusion equations indicates that the average domain area grows approximately as t 0.84 .

Ce résumé expose les affirmations des auteurs. BNTIC ne l’interprète pas comme une validation indépendante des résultats.