Scaling law in target-hunting processes

TL;DR

This paper investigates a target-hunting process modeled by a random walk with odor-based cues, revealing a scaling law between search time and distance, influenced by hunter sensitivity, with implications for animal foraging behavior.

Contribution

It introduces a novel model of odor-guided search that demonstrates a scaling law for search time depending on distance and sensitivity, advancing understanding of biological foraging processes.

Findings

Discovered a scaling law relating search time to distance

Identified the dependence of the scaling exponent on hunter sensitivity

Provided a Monte Carlo simulation framework for odor-based search processes

Abstract

We study the hunting process for a target, in which the hunter tracks the goal by smelling odors it emits. The odor intensity is supposed to decrease with the distance it diffuses. The Monte Carlo experiment is carried out on a 2-dimensional square lattice. Having no idea of the location of the target, the hunter determines its moves only by random attempts in each direction. By sorting the searching time in each simulation and introducing a variable $x$ to reflect the sequence of searching time, we obtain a curve with a wide plateau, indicating a most probable time of successfully finding out the target. The simulations reveal a scaling law for the searching time versus the distance to the position of the target. The scaling exponent depends on the sensitivity of the hunter. Our model may be a prototype in studying such the searching processes as various foods-foraging behavior of the wild animals.