Strange attractors in periodically kicked predator - prey system with discrete and distributed delay

In this paper, the behavior of rank one strange attractors in a predator - prey system with discrete and distributed delay is studied. This investigation is conducted from the perspective of a recent chaos theory of rank one maps developed by us for delayed systems. We specifically choose the well - known predator - prey system with discrete and distributed delay to demonstrate the applicability of the theory to the case of ecological systems, and prove the appearance of chaotic behavior under reasonable conditions. The results of the numerical simulations presented are in close agreement with the expectations of the theory.