循环多重网络上的分数动力学：连续时间随机游动的最优耦合和长程导航
Fractional dynamics on circulant multiplex networks: optimal coupling and long-range navigation for continuous-time random walks
摘要：
这项工作分析了分数连续时间随机游动两层复用。一个以节点为中心的动力学，其中它被假定为泊松分布的步行者成为活跃的，而跳转到它的邻居之一取决于连接权重。众所周知的拓扑结构的合成复用被用来说明通过数值模拟获得的动力学特性，而精确的解析表达式，提出了由循环层与有限数目的节点组装的复用。特别注意的是，系统的行为上的层间$D_x$和层内$D_i$系数的效果。与通常的离散时间动力学相反，弛豫时间在$D_x/D_i$的最佳值处具有明确定义的最小值。研究发现，即使在增强扩散条件下，步行者均方位移也随时间线性增加。
英文摘要：
This work analyzes fractional continuous-time random walks on two-layer multiplexes. A node-centric dynamics is used, in which it is assumed a Poisson distribution of a walker to become active, while a jump to one of its neighbors depends on the connection weight. Synthetic multiplexes with well known topology are used to illustrate dynamical features obtained by numerical simulations, while exact analytical expressions are presented for multiplexes assembled by circulant layers with finite number of nodes. Special attention is given to the effect of inter- $D_x$ and intra-layer $D_i$ coefficients on the system's behavior. In opposition to usual discrete time dynamics, the relaxation time has a well defined minimum at an optimal value of $D_x/D_i$. It is found that, even for the enhanced diffusion condition, the walkers mean square displacement increases linearly with time.
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