L\'evy-like behavior in deterministic models of intelligent agents exploring heterogeneous environments

TL;DR

This paper investigates a deterministic model of agents exploring heterogeneous environments, revealing that power-law distributions of target attractiveness can induce movement patterns similar to Lévy flights, with robustness to noise.

Contribution

It introduces a deterministic exploration model that reproduces Lévy-like movement patterns driven by power-law distributed target weights, highlighting the role of environmental heterogeneity.

Findings

Power-law target weights induce Lévy-like movement patterns.

Movement patterns are robust to added noise in disordered environments.

The model demonstrates how mental maps influence exploration dynamics.

Abstract

Many studies on animal and human movement patterns report the existence of scaling laws and power-law distributions. Whereas a number of random walk models have been proposed to explain observations, in many situations individuals actually rely on mental maps to explore strongly heterogeneous environments. In this work we study a model of a deterministic walker, visiting sites randomly distributed on the plane and with varying weight or attractiveness. At each step, the walker minimizes a function that depends on the distance to the next unvisited target (cost) and on the weight of that target (gain). If the target weight distribution is a power-law, $p(k)\sim k^{-\beta}$, in some range of the exponent $\beta$, the foraging medium induces movements that are similar to L\'evy flights and are characterized by non-trivial exponents. We explore variations of the choice rule in order to test the robustness of the model and argue that the addition of noise has a limited impact on the dynamics in strongly disordered media.