Dynamics between a predator and a prey switching two kinds of escape motions.

In nature, animals are classified into two large groups. Those that form the prey and that form the predator. A prey animal runs for its life when chased by a predatory animal. When prey animals escape from the chasing enemy, they generally use two types of evasive motion. Those are a straight-line escape motion and a zigzag-line escape motion. A fleeing prey switches between two types of evasive behavior in a manner depending on the predator's performance.I propose a mathematical model that expresses behaviors between a prey and a predator. This model brings that a straight-line escape motion is a better solution for an escape from a slow and far predator. On the other hand, an evasive motion for a near or fast enemy is a zigzag-line escape motion. This model suggests that animals have the best evasive strategy.