Chasing prey involves visual perception of the prey and running after the prey until it is caught. Visual perception involves two components, recognizing the prey and getting the direction to the prey. In this model, I shall take the recognition for granted and I shall focus on getting the direction in which to run to catch the prey.
In the example above we assume that the predator reacts to the visual information. In process control this is called feedback. The predator does not anticipate or predict where they prey is going to run.
Some level of visual tracking appears innate in phenomena such as imprinting.