Avelino P P, Bazeia D, Losano L, Menezes J, Oliveira B F
Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Sep;86(3 Pt 2):036112. doi: 10.1103/PhysRevE.86.036112. Epub 2012 Sep 17.
We investigate the population dynamics in generalized rock-paper-scissors models with an arbitrary number of species N. We show that spiral patterns with N arms may develop both for odd and even N, in particular in models where a bidirectional predation interaction of equal strength between all species is modified to include one N-cyclic predator-prey rule. While the former case gives rise to an interface network with Y-type junctions obeying the scaling law L∝t1/2, where L is the characteristic length of the network and t is the time, the latter can lead to a population network with N-armed spiral patterns, having a roughly constant characteristic length scale. We explicitly demonstrate the connection between interface junctions and spiral patterns in these models and compute the corresponding scaling laws. This work significantly extends the results of previous studies of population dynamics and could have profound implications for the understanding of biological complexity in systems with a large number of species.
我们研究了具有任意物种数量N的广义剪刀石头布模型中的种群动态。我们表明，无论N为奇数还是偶数，都可能出现具有N条臂的螺旋模式，特别是在所有物种之间等强度的双向捕食相互作用被修改为包含一个N循环捕食者 - 猎物规则的模型中。在前一种情况下，会产生一个具有Y型连接的界面网络，遵循标度律L∝t1/2，其中L是网络的特征长度，t是时间，而后者可能导致具有N条臂螺旋模式的种群网络，其特征长度尺度大致恒定。我们明确展示了这些模型中界面连接与螺旋模式之间的联系，并计算了相应的标度律。这项工作显著扩展了先前种群动态研究的结果，可能对理解具有大量物种的系统中的生物复杂性具有深远意义。
