Obstacle avoiding patterns and cohesiveness of fish school.

This paper is devoted to studying obstacle avoiding patterns and cohesiveness of fish school. First, we introduce a model of stochastic differential equations (SDEs) for describing the process of fish school's obstacle avoidance. Second, on the basis of the model we find obstacle avoiding patterns. Our observations show that there are clear four obstacle avoiding patterns, namely, Rebound, Pullback, Pass and Reunion, and Separation. Furthermore, the emerging patterns change when parameters change. Finally, we present a scientific definition for fish school's cohesiveness that will be an internal property characterizing the strength of fish schooling. There are then evidences that the school cohesiveness can be measured through obstacle avoiding patterns.