Collective Behavior of the Metric-Topological Interaction Model by Using Internal Fluctuations in the Flock

There are various views on collective animal behaviour such as birds flocking, fish schooling, and insects marching. Despite neither brain nor central control, they behave as a whole. The relation between parts and whole is needed to attack this problem because the collective behavior emerges through the interplay between individuals and the whole collective. However, the bridge between individuals and whole collective remains an open question. Recently, more accurate analysis of flocking behaviour has become possible. Cavagna and others found that fluctuations in a flock show the sizes of spatial correlations scales linearly with the size of the flock. They called this scale-invariant coherence of fluctuations "scale-free correlation." We suggest, in this paper, that scale-free correlation fills the gap between individuals' and whole flocks' movement. In a previous study, our model (metric-topological interaction model) succeeded in explaining "scale-free correlation." In this study, the MTI model shows the self-similarity of internal fluctuations and 1/ƒ fluctuation. We also show that these critical fluctuations in MTI flocks lead to flock dividing. From these results, we discuss the possibility of internal fluctuations that contribute to smooth movement as a whole flock, despite having the risk of collapsing itself.