Random walks on scale-free flowers with stochastic resetting.

Abstract

This study explores the impact of stochastic resetting on the random walk dynamics within scale-free (u,v)-flowers. Utilizing the generating function technique, we develop a recursive relationship for the generating function of the first passage time and establish a connection between the mean first passage time with and without resetting. Our investigation spans multiple scenarios, with the random walker starting from various positions and aiming to reach different target nodes, allowing us to identify the optimal resetting probability that minimizes the mean first passage time for each case. We demonstrate that stochastic resetting significantly improves search efficiency, especially in larger networks. These findings underscore the effectiveness of stochastic resetting as a strategy for optimizing search algorithms in complex networks, offering valuable applications in domains such as biological transport, data networks, and search processes where rapid and efficient exploration is vital.