Fractional dynamics on circulant multiplex networks: optimal coupling and long-range navigation for continuous-time random walks

Abstract: 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.