L\'evy-like behavior in deterministic models of intelligent agents exploring heterogeneous environments
TL;DR: Variations of the choice rule are explored 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.
read more
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.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Figures
Figure 2. Length fluctuation ratio, 〈l2〉/〈l〉2, as a function of the resource exponent β. In both the k − l/l0 and k/l rules, this quantity is maximum at β ≈ 3.1. In all cases, N = 106 and kmax = 10 3. Data was obtained from averaging over 10 different disordered media. In each realization, a walk starts near the center of the square domain and visits 105 targets, a number still ≪ N . 
Figure 3. l0 2/〈l〉2 as a function of β showing diverging steps below βc. kmax = 106, other system settings as in figure 2. 
Figure 7. Numerically computed probability Y2 (averaged over 10 4 disordered media) that two independent walkers choose the same site in the one dimensional problem with N = 107. The straight line is relation (21). 
Figure 4. Temporal evolution of the average size of the ith visited target, in the k− l rule and with β = 2.25, N = 106, kmax = 10 3. Averages are taken over 10 independent runs. 
Figure 5. Average time derivative 〈k̄i+1 − k̄i〉i performed over the time domain i = 1, ..., 104 (for the rules k − l/l0 and k/l) as a function of β. Each point is the average of ten replicas. The quantity k̄i is defined as the average value of τ consecutive ki values. Notice the onset of stationarity at β = 3. 
Figure 6. Left panel: Average energy balance as a function of β for three values of A in rule (6). Insets: Eij(t) as a function of t for β = 3 and 4 (A = 1 in both cases). Right panel: Step length distribution at fixed β = 3 and for three values of A.
Citations
Lévy foraging patterns of rural humans.
Andy M. Reynolds,Eliane Ceccon,Cristina Baldauf,Tassia Karina Medeiros,Octavio Miramontes,Octavio Miramontes +5 more
TL;DR: It is shown that Lévy walks are evident in the Me’Phaa of Mexico, in Brazilian Cariri farmers and in Amazonian farmers when gathering firewood, wild fruit and nuts, and potential generative mechanisms for the occurrence are suggested which can be used to guide future studies on human mobility.
Texture analysis using graphs generated by deterministic partially self-avoiding walks
TL;DR: This work presents an approach to generate graphs out of the trajectories produced by the tourist walks, which embody important characteristics related to tourist transitivity in the image.
48
Non-Lévy Mobility Patterns of Mexican Me’Phaa Peasants Searching for Fuel Wood
Octavio Miramontes,Octavio Miramontes,Og DeSouza,Diego Abelardo Álvarez Hernández,Eliane Ceccon,Eliane Ceccon +5 more
TL;DR: In this paper, the authors measured mobility patterns that describe walking trajectories of individual Me'Phaa peasants searching for and collecting fuel wood in the forests of "La Montana de Guerrero" in Mexico.
Human Movement Is Both Diffusive and Directed
TL;DR: This study analyses public bicycle data from central London to reveal that, although journey distances, directions, and frequencies of occurrence are spatially variable, their relative spatial patterns remain largely constant, suggesting the influence of a fixed spatial template.
26
Reorientation patterns in central-place foraging: internal clocks and klinokinesis
TL;DR: The results give experimental evidence that the internal mechanisms driving reorientations in ants tend to favour frequently long relocations, as theory predicts for efficient exploration in patchy landscapes, but ants engaged in central-place foraging can modulate such behaviour to control distances from the nest.
References
Deterministic walks as an algorithm of pattern recognition.
TL;DR: In this article, a deterministic procedure is proposed to find attractors of mutually close points based on the neighborhood ranking, and a memory parameter is used as a hierarchy parameter in which the clusters are identified.
From random walks to spin glasses
Bernard Derrida,Bernard Derrida +1 more
TL;DR: In this article, a short review on systems which exhibit non-self-averaging effects: sums of random variables when the distribution has a long tail, mean field spin glasses, random map models and returns of a random walk to the origin.
Episodic memory: what can animals remember about their past?
TL;DR: The critical features of episodic memory in humans, its relationship to declarative memory, and recent results revealing that jays can learn to perform a task that depends on certain features of Episodic memory and can thus be considered 'episodic-like' are outlined.
Tree size frequency distributions, plant density, age and community disturbance
TL;DR: It is argued that the interdependent relationships among the numerical values of a, b, NT, and D shed light on the extent to which communities have experienced recent global disturbance.
Deterministic walks in random environments
TL;DR: Deterministic walks in random environments (DWRE) occupy an intermediate position between purely random and purely deterministic (generated by deterministic dynamical systems, e.g., by maps) models of diffusion as discussed by the authors.
Related Papers (5)
David W. Sims,Emily J. Southall,Nicolas E. Humphries,Graeme C. Hays,Corey J. A. Bradshaw,Corey J. A. Bradshaw,Jonathan W. Pitchford,Alex James,Alex James,Mohammed Zaki Ahmed,Andrew S. Brierley,Mark A. Hindell,David Morritt,Michael K. Musyl,David Righton,Emily L. C. Shepard,Victoria J. Wearmouth,Rory P. Wilson,Matthew J. Witt,Julian D. Metcalfe +19 more