周期性竞争种群中靶波的出现
Emergence of target waves in paced populations of cyclically competing species
摘要：
我们研究的目标波的出现在一个周期性的捕食者-猎物模型将周期性电流的三个竞争物种在一个小区域位于中心的正方形格子。周期性电流就像一个起搏器，试图将其节奏强加给这三个物种的整体时空进化。我们表明，起搏器是能够核目标波，最终传播到整个人口，从而导致这种现象的三条路线可以区分取决于三个物种的流动性和局部电流的振荡周期。首先，目标波可以出现由于周期性电流和振荡的三个物种的密度在空间网格之间的同步。第二种方法与第一种方法相似，不同之处在于同步只是间歇性的。最后，当起搏器的频率远高于表征三个物种的整体密度的振荡时，实现了朝向目标波的第三条路线。通过考虑流动性和频率的电流作为可变参数，我们因此提供了深入了解的模式形成的机制所造成的局部和全局动态之间的相互作用，在系统中由周期性竞争物种。
英文摘要：
We investigate the emergence of target waves in a cyclic predator-prey model incorporating a periodic current of the three competing species in a small area situated at the center of the square lattice. The periodic current acts as a pacemaker, trying to impose its rhythm on the overall spatiotemporal evolution of the three species. We show that the pacemaker is able to nucleate target waves that eventually spread across the whole population, whereby three routes leading to this phenomenon can be distinguished depending on the mobility of the three species and the oscillation period of the localized current. First, target waves can emerge due to the synchronization between the periodic current and oscillations of the density of the three species on the spatial grid. The second route is similar to the first, the difference being that the synchronization sets in only intermittently. Finally, the third route towards target waves is realized when the frequency of the pacemaker is much higher than that characterizing the oscillations of the overall density of the three species. By considering mobility and the frequency of the current as variable parameters, we thus provide insights into the mechanisms of pattern formation resulting from the interplay between local and global dynamics in systems governed by cyclically competing species.
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