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.