A stochastic differential equation model for foraging behavior of fish schools

Abstract

We present a novel model of stochastic differential equations for foraging behavior of fish schools in space including obstacles. We then study the model numerically. Three configurations of space with different locations of food resource are considered. In the first configuration, fish move in free but limited space. All individuals can find food almost surely. In the second and third configurations, fish move in limited space with one or two obstacles. Our results reveal that on one hand, when school size increases, so does the probability of foraging success. On the other hand, when it exceeds an optimal value, the probability decreases. In all configurations, fish always keep a school structure through the process of foraging.