Lévy-like behavior in deterministic models of intelligent agents exploring heterogeneous environments

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 Lévy 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.

15 pages, 7 figures. One section added

References in corpus (7)

• Understanding individual human mobility patterns
• Power laws, Pareto distributions and Zipf's law
• The scaling laws of human travel
• Optimal search strategies for hidden targets
• Analytical Results for the Statistical Distribution Related to Memoryless Deterministic Tourist Walk: Dimensionality Effect and Mean Field Models
• Random walks and polymers in the presence of quenched disorder
• Accelerating random walks by disorder

Cited by in corpus (6)

• Space use by foragers consuming renewable resources
• Scaling Mobility Patterns and Collective Movements: Deterministic Walks in Lattices
• The movement of a forager: Strategies for the efficient use of resources
• Deterministic scale-invariant dynamics in a logistic Game-of-Life model
• Complex groundwater flow systems as traveling agent models
• On salesmen and tourists: two-step optimization in deterministic foragers