[3Xin2] Poster session 1

[3Xin2-101] Levy walk and Temporal Dependency in the Locomotion Data of Pill Bugs

〇Hayato Hirai¹, Ryosuke Kuribayashi¹, Utsumi Akika², Takaharu Shokaku³, Toru Moriyama², Shuji Shinohara¹ (1.Tokyo Denki University , 2.Shinshu University, 3.Meiji University)

Keywords:Levy walk, Hurst exponent, Power-law Distribution, Exponential distribution, Pill bugs

Levy walks can be seen in the migratory behavior of organisms at various levels, from bacteria and T-cells to humans. In the Levy walk, the frequency of occurrence of linear step lengths follows the power distribution p(l)~l^-μ,1<μ<3, and occasionally long-distance linear moves appear compared to the Brownian walk, which is also a type of random walk (characterized by the exponential distribution p(l)~e^-λl for the frequency of occurrence of step length l). The Levy walk is considered a useful search strategy for animals that do not know the distribution of resources scattered sparsely in the environment, and theoretically it is known to be most efficient when μ=2. In this study, we fit the gait data of the pill bugs to a certain distribution that includes our proposed exponential and power distributions as special cases and obtain the parameters of that distribution. Then, based on the parameters, we run simulations to generate a walking pattern with a step-length occurrence frequency distribution like that of the pill bugs. The Hurst index is then calculated and compared for the original gait data, the randomly shuffled data, and the step length time series data obtained by the simulation. The results confirm that there is a time dependence in the walking patterns of the pill bugs.