Prediction and classification in equation-free collective motion dynamics
Fig 2
Dynamic modes of simulated fish-schooling data.
To apply DMD to collective motions, we used a simple schooling simulation model (I) to create three different behaviors from changes in only one parameter (for details, see Materials and Methods). Then we computed the distance series with respect to nearest individuals to represent the topological relationships among individuals (II). We transformed this series into matrix form to squeeze the distance matrix. After DMD, we obtain temporal and corresponding spatial modes (III). The temporal DMD modes (A, D, G) are shown in the spectra as a function of temporal frequency. Using the results of the frequency spectra (A, D, G), we separated the spatial modes into low (0.5–1.5 Hz) and high (2–3 Hz) frequency domains. As the temporal frequency spectra, the power spectra of the spatial DMD modes for the swarm (B-C), parallel (H-I), and torus behavior (2E-F) were stronger in this order.