Random walks on complex networks under time-dependent stochastic resetting

Area of Science:

• Complex Systems
• Statistical Physics
• Network Science

Background:

• Random walks are fundamental processes on networks.
• Stochastic resetting modifies random walks by periodically returning the walker to a specific state.
• Time-dependent resetting introduces a novel layer of control over random walk dynamics.

Purpose of the Study:

• To investigate discrete-time random walks on networks with time-dependent stochastic resetting.
• To analyze how resetting probability, dependent on walker age, influences network exploration.
• To compare the efficiency of time-modulated resetting against constant resetting for search processes.

Main Methods:

• Utilizing the renewal approach for analyzing resetting processes.
• Employing spectral decomposition of the transition matrix for analytical solutions.
• Formulating stationary occupation probabilities and mean first passage times.
• Considering step-shaped and rational function-based resetting protocols.

Main Results:

• Exact solutions derived for stationary occupation probabilities and mean first passage times.
• Demonstrated theoretical results on various network structures.
• Validated findings through numerical simulations.
• Identified specific time-dependent resetting protocols that outperform constant resetting.

Conclusions:

• Time-modulated stochastic resetting offers enhanced control over random walks on networks.
• These protocols can significantly accelerate target search processes compared to static resetting.
• The age-dependent resetting strategy provides a powerful tool for optimizing network exploration dynamics.