约束Newman-Watts网络上的四态剪刀石头布博弈
Four-state rock-paper-scissors games on constrained Newman-Watts networks
摘要：
本文研究了二维约束Newman-Watts网络中三个种群的循环优势问题，该网络是一个四态的石头剪刀布游戏。通过用长程连接概率$p$限制Newman-Watts网络的最大连接距离$R_{max}$，更真实地刻画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，Monte Carlo模拟表明螺旋波的大小增加，并且系统变得不稳定，生物多样性随着$p$或$R_{max}$的增加而丧失。这些结果类似于Reichenbach \textit{et al.} [Nature（London）\textbf{448}，1046（2007）]的最近结果，其中它们仅增加迁移率而不包括长程相互作用。我们比较了有或没有长距离连接和计算空间相关函数和相关长度的解释。我们的结论是，远程连接可以提高物种的流动性，大大改变他们的交叉灭绝，使系统更加不稳定。
英文摘要：
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 $R_{max}$ in Newman-Watts networks with the long-rang 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 $R_{max}$, 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 $R_{max}$. These results are similar to recent results of Reichenbach \textit{et al.} [Nature (London) \textbf{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.
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