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Fluctuation-Driven Flocking Movement in Three Dimensions and Scale-Free Correlation

Figure 7

ADF with th variation.

(A) The graph shows the value for AFD as the threshold parameter changes. The number of individuals is fixed at 100. The threshold parameter, th, decreases or increases 0.01 radians every 100 steps. The red dots are the increasing phase, and the blue dots are the decreasing phase. The value of AFD for each dot is averaged for 100 steps with th tuning. The arrows and the number indicate the order of the process. There is an asymmetric relationship between the deceasing phase and the increasing phase. (B) The example of the explosion of the flock, projected onto a two-dimensional plane. Each individual spreads out in a radical pattern. Several steps later, the flock has divided into three sub-flocks. (C) A graph of the mean , or , for 50 times simulations from Figure 7A. The(increasing phase) is colored gray, and the (decreasing phase) is colored light gray. Error bars are SD. (D) A graph of the mean , or , for 50 times simulations from Figure 7A. The(increasing phase) is colored gray, and the(decreasing phase) is colored light gray. Error bars are SD. (E) The proportion of individual’s using the topological interaction averaged for 100 steps with th tuning in Figure 7A. All color and dots precisely correspond to Figure 7A. It can observe that there is a sharp peak at th = 0.1 radians (the point of flock’s explosion). The inset graph shows the enlarged figure in the interval th[0.4,1.0]. (F) The frequency of individual’s switching between two interactions averaged for 100 steps with th tuning in Figure 7A. All color and dots precisely correspond to Figure 7A. The inset graph shows the enlarged figure in the interval th[0.4,1.0]. The switching events between two interactions in the increasing phase are more longstanding than one in the decreasing phase.

doi: https://doi.org/10.1371/journal.pone.0035615.g007