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Random walks on scale-free flowers with stochastic resetting.

Anlin Li¹, Xiaohan Sun¹, Shaoxiang Zhu¹

¹School of Mathematical Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China.

Chaos (Woodbury, N.Y.)

|January 10, 2025

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Stochastic resetting enhances random walk search efficiency in complex networks. This method optimizes navigation by minimizing the mean first passage time, proving vital for large-scale systems.

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Area of Science:

Complex network dynamics
Statistical physics of transport phenomena

Background:

Random walks are fundamental models for exploring networks.
Scale-free networks exhibit unique structural properties influencing diffusion.
Stochastic resetting is a strategy to enhance search efficiency.

Purpose of the Study:

To investigate the effect of stochastic resetting on random walk dynamics in scale-free (u,v)-flowers.
To analyze how resetting influences first passage time and search efficiency.
To identify optimal resetting strategies for different network configurations.

Main Methods:

Utilizing the generating function technique to derive a recursive relationship for first passage time.
Calculating the mean first passage time with and without resetting.
Exploring various starting positions and target nodes.

Main Results:

A direct connection was established between mean first passage times with and without resetting.
Optimal resetting probabilities were identified for different scenarios.
Stochastic resetting was shown to significantly improve search efficiency, particularly in larger networks.

Conclusions:

Stochastic resetting is an effective strategy for optimizing search algorithms in complex networks.
The findings have implications for biological transport, data networks, and efficient search processes.
This approach offers a method for rapid and efficient exploration in complex systems.