Lopez Cristobal, Hernandez-Garcia Emilio, Piro Oreste, Vulpiani Angelo, Zambianchi Enrico
Instituto Mediterraneo de Estudios Avanzados (IMEDEA), E-07071 Palma de Mallorca, SpainDipartimento di Fisica, Universita di Roma "La Sapienza," P.le A. Moro 2, I-00185, Roma, Italy.
Chaos. 2001 Jun;11(2):397-403. doi: 10.1063/1.1371285.
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 fluid particles are advected by a two-dimensional symplectic map possibly yielding Lagrangian chaos. Each 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. (c) 2001 American Institute of Physics.
研究了由二维混沌流体流输运的反应演化场的离散时间模型。我们的方法基于使用拉格朗日格式，其中流体粒子由可能产生拉格朗日混沌的二维辛映射进行平流。每个流体粒子携带活性物质的浓度，这些浓度根据其自身的反应动力学而演化。这种演化也用映射来建模。受海洋生态学中相关问题的启发，即营养物质或猎物的局部分布如何影响由流体流输运的捕食者的空间结构，我们研究了一个特定模型，其中种群动态由具有空间依赖系数的逻辑斯谛映射给出，平流由标准映射给出。在不同条件下获得了捕食者欧拉空间浓度中的分形和随机模式。利用这个耦合映射（平流加反应）系统与随机映射的类比，讨论了这些模式的一些特征。(c) 2001美国物理研究所。
