Various collective behavior in swarm oscillator model

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. ► A long-time behavior of a group of chemotactic elements is numerically studied. ► The system exhibits various collective motions depending on the two parameters. ► The collective motions are classified into thirteen kinds of phase. ► The two parameters indicate the time required to the two responses of the element. ► We obtained the phase diagram in those parameter space.