Predator-prey system with seasonally varying additional food to predators

We have proposed a three species food chain model with additional food
to predators. We have studied the dynamics of this predator-prey model with seasonally varying additional food to predators. Bifurcation analysis of the proposed model is done with respect to quality and quantity of additional food, amplitude of oscillation and angular frequency of oscillations. The bifurcation analysis of our model revealed the vital role of seasonality parameters in the controllability of the predator-prey system. Our analysis predicts that seasonality parameters are very important to determine the quality and quantity of additional food for controlling the dynamics of a food chain model.