Emergence of autocatalytic reaction in a meme propagation model based on particle motion

Meme refers to a unit of human cultural transmission, analogous to biological evolution. Meme propagation has an autocatalytic property in the sense that it increases its reproductive rate by duplicating the source of propagation. The purpose of this study is to gain general knowledge about the dynamics of meme propagation. This paper presents a minimal model based on the physical movement of particles for investigating the relationship between the behavior of the hosts (velocity of particles) and the autocatalytic property of the meme. It is demonstrated that two extreme memes, the fastest and the slowest ones, have a strong tendency to survive by autocatalytic properties at individual and aggregate levels, respectively, although all memes seem neutral in terms of fitness in the model definition.