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Topological Data Analysis of Biological Aggregation Models

Fig 6

Aggregate behavior of the Vicsek model, simulation #1.

The simulation that generated these data was seeded with the initial condition in Fig 5(A) and a typical snapshot is shown in Fig 7(A). (A) Normalized average velocity order parameter φ(t). (B) Contour plot of Betti number ${\mathsf{\text{b}}}_0(\varepsilon ,t)$. (C) Contour plot of Betti number ${\mathsf{\text{b}}}_1(\varepsilon ,t)$. The topological analysis reveals dynamics not captured by the order parameter, namely cluster formation and the loss of topological circles consistent with particles aligning and covering only one dimension of the periodic simulation domain. See text for a more comprehensive analysis.

doi: https://doi.org/10.1371/journal.pone.0126383.g006