Proxitaxis: An adaptive search strategy based on proximity and stochastic resetting

Area of Science:

• Physics
• Mathematics
• Computational Science

Background:

• Search strategies often require directional information, limiting applicability in scenarios with only distance cues.
• Understanding optimal search patterns is crucial for fields ranging from biology to robotics.

Purpose of the Study:

• Introduce and analyze "proxitaxis," a novel search strategy relying solely on distance to the target.
• Determine if this strategy can be optimized for maximum target capture probability.
• Investigate the occurrence and nature of phase transitions within the optimal strategy.

Main Methods:

• Analytical computation of target capture probability.
• Modeling the strategy with distance-dependent diffusion and stochastic resetting.
• Dynamic updating of the resetting position during the search.

Main Results:

• Proxitaxis strategy analytically characterized.
• Capture probability maximization achieved through optimal control parameter selection.
• Multiple, generic phase transitions observed in the optimal strategy across dimensions.

Conclusions:

• Proxitaxis offers an effective search paradigm when only distance information is available.
• Optimal control parameters are key to maximizing search efficiency.
• The identified phase transitions highlight fundamental properties of this search strategy.