Random walks on complex networks under time-dependent stochastic resetting

Abstract

We study discrete-time random walks on networks subject to a time-dependent stochastic resetting, where the walker either hops randomly between neighboring nodes with a probability $1-\varphi (a)$, or is reset to a given node with a complementary probability $\varphi (a)$. The resetting probability $\varphi (a)$ depends on the time $a$ since the last reset event (also called $a$ the age of the walker). Using the renewal approach and spectral decomposition of transition matrix, we formulize the stationary occupation probability of the walker at each node and the mean first passage time between arbitrary two nodes. Concretely, we consider that two different time-dependent resetting protocols that are both exactly solvable. One is that $\varphi (a)$ is a step-shaped function of $a$ and the other one is that $\varphi (a)$ is a rational function of $a$. We demonstrate the theoretical results on two different networks, also validated by numerical simulations, and find that the time-modulated resetting protocols can be more advantageous than the constant-probability resetting in accelerating the completion of a target search process.

arXiv comment10 pages, 3 figures. arXiv admin note: text overlap with arXiv:2105.08323

References in corpus (72)

• Emergence of scaling in random networks
• Understanding individual human mobility patterns
• Maps of random walks on complex networks reveal community structure
• Epidemic processes in complex networks
• Vital nodes identification in complex networks
• Human Mobility: Models and Applications
• Reaction-diffusion processes and metapopulation models in heterogeneous networks
• Diffusion with Stochastic Resetting
• Intermittent search strategies
• Voter Model on Heterogeneous Graphs
• Random walks and diffusion on networks
• Stochastic Resetting and Applications
• Diffusion with Optimal Resetting
• First Passage Under Restart
• Optimal stochastic restart renders fluctuations in first passage times universal
• Experimental realization of diffusion with stochastic resetting
• Diffusion under time-dependent resetting
• Run and tumble particle under resetting: a renewal approach
• Diffusion in a potential landscape with stochastic resetting
• Optimal mean first-passage time for a Brownian searcher subjected to resetting: experimental and theoretical results
• Diffusion with resetting in arbitrary spatial dimension
• Diffusion with stochastic resetting at power-law times
• Localization of maximal entropy random walk
• Random walks with preferential relocations to places visited in the past and their application to biology
• Non-equilibrium steady states of stochastic processes with intermittent resetting
• Fluctuating interfaces subject to stochastic resetting
• Natural human mobility patterns and spatial spread of infectious diseases
• The Michaelis-Menten reaction scheme as a unified approach towards the optimal restart problem
• WKB theory of large deviations in stochastic populations
• Google matrix analysis of directed networks
• Stochastic thermodynamics of resetting
• Large deviations for Markov processes with resetting
• Random walks on weighted networks
• Resetting processes with non-instanteneous return
• Effects of refractory period on stochastic resetting
• The inspection paradox in stochastic resetting
• First passage of a particle in a potential under stochastic resetting: a vanishing transition of optimal resetting rate
• Work fluctuations and Jarzynski equality in stochastic resetting
• Optimization in First-Passage Resetting
• Random walks on networks with stochastic resetting
• Integral Fluctuation Theorems for Stochastic Resetting Systems
• Symmetric Exclusion Process under Stochastic Resetting
• Stochastic resetting with stochastic returns using external trap
• Ising model with stochastic resetting
• Epidemic extinction and control in heterogeneous networks
• Run-and-Tumble particles in Two-dimensions under Stochastic Resetting
• Spectral properties of simple classical and quantum reset processes
• Random walks in weighted networks with a perfect trap: An application of Laplacian spectra
• First passage under restart for discrete space and time: application to one dimensional confined lattice random walks
• Invariants of motion with stochastic resetting and space-time coupled returns
• Active Brownian Motion in two-dimensions under Stochastic Resetting
• Mean first passage time of active Brownian particle in one dimension
• Extremal statistics for stochastic resetting systems
• Occupation time of a run-and-tumble particle with resetting
• Mean perimeter and area of the convex hull of a planar Brownian motion in the presence of resetting
• Record statistics for random walks and Lévy flights with resetting
• Stochastic resetting on comb-like structures
• Diffusive transport on networks with stochastic resetting to multiple nodes
• First-passage Brownian functionals with stochastic resetting
• Number of distinct sites visited by a resetting random walker
• Phase transition in non-Markovian animal exploration model with preferential returns
• Random walks on complex networks with first-passage resetting
• From classical to quantum walks with stochastic resetting on networks
• Robust random search with scale-free stochastic resetting
• First passage of a diffusing particle under stochastic resetting in bounded domains with spherical symmetry
• Random walks on complex networks under node-dependent stochastic resetting
• Maximum and records of random walks with stochastic resetting
• Drift-diffusion on a Cayley tree with stochastic resetting: the localization-delocalization transition
• Random walks on complex networks with multiple resetting nodes: a renewal approach
• Exploring complex networks by means of adaptive walkers
• Discrete-time random walks and Lévy flights on arbitrary networks: when resetting becomes advantageous?
• Random Walks on Complex Networks

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