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

Abstract

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.

22 pages, 5 figures

References in corpus (5)

• Analytical and Numerical Studies of Noise-induced Synchronization of Chaotic Systems
• Smooth-filamental transition of active tracer fields stirred by chaotic advection
• Synchronization of Chaotic Maps by Symmetric Common Noise
• The multifractal structure of chaotically advected chemical fields
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Cited by in corpus (6)

• Frontiers of chaotic advection
• Analytical and Numerical Studies of Noise-induced Synchronization of Chaotic Systems
• Biological activity in the wake of an island close to a coastal upwelling
• Small-scale structure of nonlinearly interacting species advected by chaotic flows
• Noise and Inertia-Induced Inhomogeneity in the Distribution of Small Particles in Fluid Flows
• Spatial Patterns in Chemically and Biologically Reacting Flows