具有淬火无序的有向图上循环竞争种群的固定
Fixation in cyclically competing species on a directed graph with quenched disorder
摘要：
提出了一个简单的有向图上具有淬火无序的循环竞争物种模型，作为石头剪刀布模型的推广。通过假设有向随机图中的回路的影响在热力学极限下可以忽略，证明了对于任何有限无序，当物种数$s$大于空间连通度$c$时，系统固定于冻结构型，否则保持活跃.一个网站永远不会改变其状态的持久性概率的非平凡的下限和上限也解析计算。所得到的边界和数值模拟支持存在的相变作为$1<c_l(s)\le c <s$的无序的函数，与$s$依赖的阈值的连接$c_l(s)$。
英文摘要：
A simple model of cyclically competing species on a directed graph with quenched disorder is proposed as an extension of the rock-paper-scissors model. By assuming that the effects of loops in a directed random graph can be ignored in the thermodynamic limit, it is proved for any finite disorder that the system fixates to a frozen configuration when the species number $s$ is larger than the spatial connectivity $c$, and otherwise stays active. Nontrivial lower and upper bounds for the persistence probability of a site never changing its state are also analytically computed. The obtained bounds and numerical simulations support the existence of a phase transition as a function of disorder for $1<c_l(s)\le c <s$, with a $s$-dependent threshold of the connectivity $c_l(s)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
