A simulation of grouping: an aggregating random walk

We have developed a Lagrangian model making use of an application of the Auto-Regressive (AR) model to simulate organism aggregation. Our model stems from the dynamical consideration of organism grouping. A correlated walk based on the second-order AR model has an analogous autocorrelation function with the dynamically derived autocorrelation function for aggregating animals studied by the second author. However, the correlated walk fails to exhibit an aggregating feature in the variance of animal locations. We have introduced an interacting term with the nearest neighbour in the correlating walk model. The variance of animal locations initially increases at a much higher rate than the conventional turbulence dispersion. At an intermediate stage, the variance remains at a finite value for a long time, showing aggregating characteristics.