Periodic solution of a periodic prey-predator model with variable carrying capacity

Commonly, it is assumed that the carrying capacity is constant in the conventional predator-prey model. In contrast, we investigate a predator-prey scenario which have a common prey in this work, the carrying capacity of the predator and the prey are variables changing with the amount of common prey which consumed by both predator and prey. We were able to establish the necessary requirements in favor of asymptotic stability globally and uniqueness of periodic solutions.