Fig 3. Examples of animal motion studied in this paper.

The examples vary in complexity, in the dimension of the physical / behavioral space, and in the number of interacting individuals. (A) Single ant or several interacting ants with three behavioral states moving in 1D. (B) Bacteria climbing a chemical gradient in 2D using a run-and-tumble motion. The position space is three dimensional (two spatial coordinates plus the direction). The “tumble state” in which bacteria perform directional random walk is a compound state constructed from quick random switches between “tumble right” and “tumble left” states with deterministic laws of motion. (C) Two tracked interacting zebrafish moving in 2D in a shallow water tank. The motion can be split into three kinematic states (shown later): the passive state in which fish does not actively contribute to the motion, and two active states (left/right) where the action of fish results in positive acceleration and change of direction to either left or right direction. The rates of switching between the three kinematic states are assumed to depend on up to three kinematic variables.