TY - JOUR

T1 - Weber-Fechner relation and Lévy-like searching stemmed from ambiguous experiences

AU - Sakiyama, T.

AU - Gunji, Y. P.

N1 - Funding Information:
The authors thank the Japan Society for the Promotion of Science for financial support ( B2130093 ).
Publisher Copyright:
© 2015 Elsevier B.V.

PY - 2015/7/18

Y1 - 2015/7/18

N2 - Abstract Here, we show that an optimized Lévy-like walk (μ≈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.

AB - Abstract Here, we show that an optimized Lévy-like walk (μ≈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.

KW - Power-law

KW - Random walk

KW - Weber-Fechner's law

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U2 - 10.1016/j.physa.2015.06.038

DO - 10.1016/j.physa.2015.06.038

M3 - Article

AN - SCOPUS:84937212331

VL - 438

SP - 161

EP - 168

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

M1 - 16269

ER -