Population dynamics advected by chaotic flows: A discrete-time map approach

A discrete-time model of reacting evolving fields, transported by a bidimen sional chaotic fluid flow, is studied. Our approach is based on the use of a Lagrangian scheme where fluid particles are advected by a two-dimensional symplectic map possibly yielding Lagrangian chaos. Each fluid particle car ries concentrations of active substances which evolve according to its own reaction dynamics. This evolution is also modeled in terms of maps. Motivat ed by the question, of relevance in marine ecology, of how a localized dist ribution of nutrients or preys affects the spatial structure of predators t ransported by a fluid flow, we study a specific model in which the populati on dynamics is given by a logistic map with space-dependent coefficient, an d advection is given by the standard map. Fractal and random patterns in th e Eulerian spatial concentration of predators are obtained under different conditions. Exploiting the analogies of this coupled-map (advection plus re action) system with a random map, some features of these patterns are discu ssed. (C) 2001 American Institute of Physics.