群振動子系(解析・予測・制御流体数理(3),一般講演)

概要

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There exists a wide variety of physical and biological systems consisting of motile elements whose internal degrees of freedom interact with their collective macroscopic or mesoscopic order. Here, we study collective emergent structures of motile dynamical elements in a unified manner, ignoring system-specific details. As perhaps the simplest model of motile dynamical elements, we propose a general model of gradient-taxis oscillators. From this model, we derive a novel class of normal form describing the phases and positions of the oscillators by means of center-manifold reduction and phase reduction methods. The model obtained through these reductions is quite universal, and we find that it exhibits a rich variety of patterns. This richness is due to the fact that the interaction between elements can be attractive or repulsive, depending on the internal states and positions of the elements.
2009-09-02