Zhang Guo-Yong, Chen Yong, Qi Wei-Kai, Qing Shao-Meng
Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jun;79(6 Pt 1):062901. doi: 10.1103/PhysRevE.79.062901. Epub 2009 Jun 2.
We study the cyclic dominance of three species in two-dimensional constrained Newman-Watts networks with a four-state variant of the rock-paper-scissors game. By limiting the maximal connection distance Rmax in Newman-Watts networks with the long-range connection probability p , we depict more realistically the stochastic interactions among species within ecosystems. When we fix mobility and vary the value of p or Rmax, the Monte Carlo simulations show that the spiral waves grow in size, and the system becomes unstable and biodiversity is lost with increasing p or Rmax. These results are similar to recent results of Reichenbach et al. [Nature (London) 448, 1046 (2007)], in which they increase the mobility only without including long-range interactions. We compared extinctions with or without long-range connections and computed spatial correlation functions and correlation length. We conclude that long-range connections could improve the mobility of species, drastically changing their crossover to extinction and making the system more unstable.
我们用剪刀石头布游戏的四态变体，研究二维受限纽曼 - 瓦特网络中三种物种的循环优势。通过在具有长程连接概率(p)的纽曼 - 瓦特网络中限制最大连接距离(R_{max})，我们更现实地描绘了生态系统中物种间的随机相互作用。当我们固定迁移率并改变(p)或(R_{max})的值时，蒙特卡罗模拟表明螺旋波尺寸增大，并且随着(p)或(R_{max})的增加，系统变得不稳定且生物多样性丧失。这些结果与赖兴巴赫等人[《自然》（伦敦）448, 1046 (2007)]最近的结果相似，在他们的研究中仅增加了迁移率而未包括长程相互作用。我们比较了有无长程连接时的灭绝情况，并计算了空间相关函数和相关长度。我们得出结论，长程连接可以提高物种的迁移率，极大地改变它们向灭绝的转变并使系统更不稳定。
