Araújo Sabrina B L, de Aguiar M A M
Instituto de Física "Gleb Wataghin," Universidade Estadual de Campinas, Caixa Postal 6165, 13083-970 Campinas, São Paulo, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jun;75(6 Pt 1):061908. doi: 10.1103/PhysRevE.75.061908. Epub 2007 Jun 14.
We study the dynamics of populations of predators and preys using a mean field approach and a spatial model. The mean field description assumes that the individuals are homogeneously mixed and interact with one another with equal probability, so that space can be ignored. In the spatial model, on the other hand, predators can prey only in a certain neighborhood of their spatial location. We show that the size of these predation neighborhoods has dramatic effects on the dynamics and on the organization of the species in space. In the case of a three species food chain, in particular, the populations of predators display a sequence of apparently irregular outbreaks when the predation neighborhood has intermediate values, as compared to the size of the available space. Nonetheless, further increasing their size makes the outbreaks disappear and the dynamics approach that of the mean field model. Our study of synchronization also shows that the periodic behavior displayed by the average populations in a spatially extended system may hide the existence of patches that oscillate out of phase in a highly coordinated fashion.
我们使用平均场方法和空间模型来研究捕食者和猎物种群的动态。平均场描述假设个体均匀混合并以相等的概率相互作用，因此可以忽略空间因素。另一方面，在空间模型中，捕食者只能在其空间位置的特定邻域内捕食。我们表明，这些捕食邻域的大小对动态以及物种在空间中的组织具有显著影响。特别是在三物种食物链的情况下，与可用空间的大小相比，当捕食邻域具有中间值时，捕食者种群会出现一系列明显不规则的爆发。然而，进一步增大其大小会使爆发消失，动态趋近于平均场模型。我们对同步的研究还表明，在空间扩展系统中平均种群所表现出的周期性行为可能掩盖了以高度协调方式异相振荡的斑块的存在。
