Szabó György, Arial Sznaider Gustavo
Research Institute for Technical Physics and Materials Science, PO Box 49, H-1525 Budapest, Hungary.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Mar;69(3 Pt 1):031911. doi: 10.1103/PhysRevE.69.031911. Epub 2004 Mar 31.
We study a four-species ecological system with cyclic dominance whose individuals are distributed on a square lattice. Randomly chosen individuals migrate to one of the neighboring sites if it is empty or invade this site if occupied by their prey. The cyclic dominance maintains the coexistence of all four species if the concentration of vacant sites is lower than a threshold value. Above the threshold, a symmetry breaking ordering occurs via growing domains containing only two neutral species inside. These two neutral species can protect each other from the external invaders (predators) and extend their common territory. According to our Monte Carlo simulations the observed phase transition seems to be equivalent to those found in spreading models with two equivalent absorbing states although the present model has continuous sets of absorbing states with different portions of the two neutral species. The selection mechanism yielding symmetric phases is related to the domain growth process with wide boundaries where the four species coexist.
我们研究了一个具有循环优势的四物种生态系统，其个体分布在一个正方形晶格上。如果相邻位点为空，随机选择的个体会迁移到该位点；如果被其猎物占据，则会入侵该位点。如果空位浓度低于阈值，循环优势会维持所有四个物种的共存。高于阈值时，会通过内部仅包含两个中性物种的生长域发生对称破缺排序。这两个中性物种可以相互保护免受外部入侵者（捕食者）的侵害，并扩展它们的共同领地。根据我们的蒙特卡罗模拟，观察到的相变似乎与在具有两个等效吸收态的扩散模型中发现的相变相当，尽管当前模型具有连续的吸收态集，其中两个中性物种的比例不同。产生对称相的选择机制与四种物种共存的宽边界域生长过程有关。
