Fish schools

The Persistent Turner model

Experimental measurements of fish trajectories (J. Gautrais et al, J. Math. Biol. (2009) 58: 429-445) suggest that individual fish behaviour follows the 'Persistent Turner' (PT) process.

The PT model assumes that individual trajectories consist of pieces of circles with randomly varying radii, which are patched together (see left picture).

The right picture compares the measurements to the model for a single fish trajectory (top: measurement (courtesy of G. Theraulaz); bottom: simulation).

For non-interacting individuals, the large scale dynamics of this process is of diffusion type, with an analytically computable diffusion constant.

Interactions express the trend of the fish to turn towards the mean flow direction ('a la Vicsek'). The macroscopic dynamics is described by the Self-Organized Hydrodynamic (SOH) model. The correspondance between the parameters of the SOH and PT models is explicit.

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