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

Lopez, Cristobal; Hernandez-Garcia, Emilio; Piro, Oreste; Vulpiani, Angelo; Zambianchi, Enrico
CHAOS 11, 397-403 (2001)

A discrete-time model of reacting evolving
fields, transported by a bidimensional chaotic fluid flow, is
studied. Our approach is based on the use of a Lagrangian scheme
where {it fluid particles} are advected by a $2d$ symplectic map
possibly yielding Lagrangian chaos. Each {it fluid particle}
carries concentrations of active substances which evolve according
to its own reaction dynamics. This evolution is also
modeled in terms of maps. Motivated by the question, of relevance
in marine ecology, of how a localized distribution of nutrients or
preys affects the spatial structure of predators transported by a
fluid flow, we study a specific model in
which the population dynamics is given by a logistic map with
space-dependent coefficient, and advection is given by the
standard map. Fractal and random patterns in the Eulerian spatial
concentration of predators are obtained under different
conditions. Exploiting the analogies of this coupled-map
(advection plus reaction) system with a random map, some features
of these patterns are discussed.

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