Adjusting the Trapping Process of a Directed Weighted Edge-Iteration Network - Su, Jing; Ma, Mingyuan; Zhang, Mingjun; Yao, Bing (Frontiers in Physics, 2022)
Controlling the trapping process is one of the important themes in the study of random walk in real complex systems. We study two types of random walks that are different from the traditional random walk on a directed weighted network. The first type of random walk is weighted random walk controlled by the weight $θ$, the other is delayed-weighted random walk affected by both delay probability $p$ and weight $θ$. Further, we derive analytically the average trapping time (ATT) measuring the efficiency of the two types of trapping processes, the result shows that ATT grows sub-linearly, linearly, super-linearly with network order when the weight satisfies $θ< \frac{3}{2}$, $θ=\frac{3}{2}$ and $θ>\frac{3}{2}$ respectively. The weight $θ$ of the directed network can be adjusted by direction, the delay parameter $p$ only change the prefactor of the ATT, and the weight $θ$ modifies both the prefactor and scaling of the ATT.