Dynamic Modeling of Discrete Biologics for Active Sonar Simulation

In this paper, we propose a simple model for simulating the group dynamics of aggregate, discrete biologics in active undersea sonar. Using a Lagrangian representation, group behavior is modeled by a set of Newtonian forces and stochastic perturbations on a collection of point masses. Interactions comprise a grouping force, which gives a characteristic separation distance, and an arrayal force, which tends to align the velocities of the group's constituents. The model is similar to previous attempts to model fish schools but contains only six parameters: three that are physical and three that are behavioral in nature. We characterize the group dynamics in terms of their statistical and asymptotic properties and study these as a function of the model parameters. The key result is a set of predictions for the asymptotic speed and separation distance in terms of the model parameters.