Search

The swarm oscillator model describes the long-time behavior of interacting chemotactic particles, and it shows numerous types of macroscopic patterns. However, the reason why so many kinds of patterns emerge is not clear. In this study, we elucidate the mechanism underlying the diversity of the pattens by analyzing the model for two particles. Focusing on the behavior when the two particles are spatially close, we find that the dynamics is classified into eight types, which explain most of the observed 13 types of patterns.

We numerically investigate the swarm oscillator model, which describes a long-time asymptotic behavior of chemotactic elements [D. Tanaka, Phys. Rev. Lett. 99 (2007) 134103]. As many as thirteen kinds of collective behavior are observed for various sets of specific two parameters in the model. Those two parameters imply the time delays from the stimulation on an element by the field that intermediates the interaction between elements to the two kinds of responses of the element. The analysis of the two-element system clarifies why some phases and phase boundaries emerge.

We investigate what is called swarm oscillator model where interacting motile oscillators form various kinds of ordered structures. We particularly focus on the dimensionality of clusters which oscillators form. In two-dimensional space, oscillators spontaneously form one-dimensional clusters or two-dimensional clusters. By studying the three-oscillator system, we analytically find the conditions of the appearance of those patterns. The validity of those conditions in applying to systems of more oscillators is demonstrated by numerically investigating a system of twenty oscillators.

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.