Lévy Walk in Swarm Models Based on Bayesian and Inverse Bayesian Inference

Yukio-Pegio Gunji; Takeshi Kawai; Hisashi Murakami; Takenori Tomaru; Mai Minoura; Shuji Shinohara

doi:10.1016/j.csbj.2020.11.045

Lévy Walk in Swarm Models Based on Bayesian and Inverse Bayesian Inference

Comput Struct Biotechnol J. 2020 Dec 8:19:247-260. doi: 10.1016/j.csbj.2020.11.045. eCollection 2021.

Authors

Yukio-Pegio Gunji¹, Takeshi Kawai¹, Hisashi Murakami², Takenori Tomaru¹, Mai Minoura¹, Shuji Shinohara³

Affiliations

¹ Department of Intermedia Art and Science, School of Fundamental Science and Technology, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, 169-8555, Japan.
² Research Center for Advanced Science and Technology, The University of Tokyo Komaba 4-6-1, Meguro-ku, Tokyo, 153-0041, Japan.
³ Department of Bioengineering, Graduate School of Engineering, The University of Tokyo Hongo 7-3-1, Bunkyo-ku, Tokyo, 113-0033, Japan.

Abstract

While swarming behavior is regarded as a critical phenomenon in phase transition and frequently shows the properties of a critical state such as Lévy walk, a general mechanism to explain the critical property in swarming behavior has not yet been found. Here, we address this problem with a simple swarm model, the Self-Propelled Particle (SPP) model, and propose a way to explain this critical behavior by introducing agents making decisions via the data-hypothesis interaction in Bayesian inference, namely, Bayesian and inverse Bayesian inference (BIB). We compare three SPP models, namely, the simple SPP, the SPP with Bayesian-only inference (BO) and the SPP with BIB models. We show that only the BIB model entails coexisting tornado, splash and translation behaviors, and the Lévy walk pattern.

Keywords: Bayesian inference; Critical phenomena; Lévy walk; Swarm Behavior.