Auger P, Poggiale J C
UMR CNRS 5558, Université Claude Bernard Lyon-1, Villeubanne, France.
J Theor Biol. 1996 Sep 21;182(2):99-108. doi: 10.1006/jtbi.1996.0145.
We present aggregation and emergence methods in large-scale dynamical systems with different timescales. Aggregation corresponds to the reduction of the dimension of a dynamical system which is replaced by a smaller model for a small number of global variables at a slow timescale. We study the couplings between fast and slow dynamics leading to the emergence of global properties in the aggregated model. First, we study the case of a single population in a patchy environment. Growth rates are assumed to be linear on each patch. Individuals can migrate from one patch to another at a fast timescale. We choose different density dependent migration processes. In each case, we use aggregation methods to obtain the corresponding growth equation for the total density of the population at a slow timescale. We look for particular density dependent migration processes leading to an aggregated logistic-like equation. Second, we study the case of two interacting populations. A particular choice of density dependent migrations leads to an aggregated competition model.
我们展示了具有不同时间尺度的大规模动力系统中的聚集和涌现方法。聚集对应于动力系统维度的降低，该动力系统在慢时间尺度上由一个针对少量全局变量的较小模型所取代。我们研究快速和慢速动力学之间的耦合，这导致了聚集模型中全局性质的涌现。首先，我们研究斑块环境中单个种群的情况。假设每个斑块上的增长率是线性的。个体可以在快速时间尺度上从一个斑块迁移到另一个斑块。我们选择不同的密度依赖迁移过程。在每种情况下，我们使用聚集方法来获得慢时间尺度上种群总密度的相应增长方程。我们寻找导致聚集的类似逻辑斯谛方程的特定密度依赖迁移过程。其次，我们研究两个相互作用种群的情况。对密度依赖迁移的一种特定选择导致了一个聚集竞争模型。
