Diffusive transport on networks with stochastic resetting to multiple nodes

TL;DR

This paper develops a spectral method to analyze how stochastic resetting to multiple nodes affects diffusive transport and search efficiency on various networks, including rings, comb graphs, and regular networks.

Contribution

It introduces a general formalism for calculating stationary and first passage times for Markovian random walks with multiple resetting nodes, applicable to diverse network structures.

Findings

Resetting to multiple nodes can optimize search times on networks.

Analytical expressions derived for various network topologies.

Resetting influences the exploration efficiency of random walks.

Abstract

We study the diffusive transport of Markovian random walks on arbitrary networks with stochastic resetting to multiple nodes. We deduce analytical expressions for the stationary occupation probability and for the mean and global first passage times. This general approach allows us to characterize the effect of resetting on the capacity of random walk strategies to reach a particular target or to explore the network. Our formalism holds for ergodic random walks and can be implemented from the spectral properties of the random walk without resetting, providing a tool to analyze the efficiency of search strategies with resetting to multiple nodes. We apply the methods developed here to the dynamics with two reset nodes and derive analytical results for normal random walks and L\'evy flights on rings. We also explore the effect of resetting to multiple nodes on a comb graph, L\'evy flights that visit specific locations in a continuous space, and the Google random walk strategy on regular networks.