title: Hierarchical cluster structures in a one-dimensional swarm oscillator model.
abstract: Swarm oscillator model derived by one of the authors (Tanaka), where interacting motile elements form various kinds of patterns, is investigated. We particularly focus on the cluster patterns in one-dimensional space. We mathematically derive all static and stable configurations in final states for a particular but a large set of parameters. In the derivation, we introduce renormalized expression of this model. We find that the static final states are hierarchical cluster structures in which a cluster consists of smaller clusters in a nesting manner.
authors.affiliation: Department of Complex Systems Science, Graduate School of Information Science, Nagoya University, Nagoya 464-8601, Japan. miwasa@r.phys.nagoya-u.ac.jp
authors.forename: Masatomo
authors.initials: M
authors.lastname: Iwasa
authors.forename: Kazuki
authors.initials: K
authors.lastname: Iida
authors.forename: Dan
authors.initials: D
authors.lastname: Tanaka