Predicting search time when hunting for multiple moving targets: A recursive harmonic law.

Area of Science:

• Network science
• Search theory
• Stochastic processes

Background:

• Searching for mobile targets is crucial in various fields.
• Quantifying search efficiency for multiple, moving targets presents significant challenges.
• Existing models often simplify target behavior or network complexity.

Purpose of the Study:

• To introduce a novel metric, mean random search time (MRST), for quantifying multi-target search efficiency on networks.
• To analyze the relationship between the number of targets and search time.
• To uncover the underlying mathematical principles governing multi-target search dynamics.

Main Methods:

• Development of the mean random search time (MRST) metric.
• Analysis of MRST averaged over all initial conditions (global MRST).
• Derivation of a recursive harmonic law to describe MRST growth.

Main Results:

• Global MRST follows a recursive harmonic law relative to single-target search.
• When target diffusion laws are identical, global MRST increases logarithmically with the number of targets.
• The recursive harmonic law accurately predicts time intervals between capturing successive targets.

Conclusions:

• The recursive harmonic law provides a fundamental understanding of multi-target search on networks.
• MRST offers a robust measure for search strategy optimization in dynamic environments.
• This work lays the groundwork for more sophisticated analysis of complex search problems.