Weber-Fechner relation and Levy-like searching stemmed from ambiguous experiences

Authored by T Sakiyama, Y P Gunji

Date Published: 2015

DOI: 10.1016/j.physa.2015.06.038

Sponsors: Japanese Society for the Promotion of Science (JSPS)

Platforms: No platforms listed

Model Documentation: Other Narrative Flow charts Mathematical description

Model Code URLs: Model code not found

Abstract

Here, we show that an optimized Levy-like walk (mu approximate to 2.00) and the Weber Fechner law can be achieved in our new multi-agent based model that depends on step lengths. Weber Fechner equation is strongly related to power-law. This equation is sometimes used in order to obtain power-law tailed distributions in observational levels. However, no study has reported how these two popular equations were achieved in micro or mechanistic levels. We propose a new random walk algorithm based on a re-valued algorithm, in which an agent has limited memory capacity, i.e., an agent has a memory of only four recent random numbers (limitation number). Using these random numbers, the agent alters the directional heuristic if the agent experiences moving directional biases. In this paper, the initial limitation number varies depending on the interaction among agents. Thus, agents change their limitation number and produce time delay in respect to rule change events. We show that slope values are variable compared with isolate foraging even though both indicate power-law tailed walks derived from Weber Fechner equation. (C) 2015 Elsevier B.V. All rights reserved.

Tags

explanation law information context Walk movement patterns Perception Odometry