Dynamics of a Non-autonomous Prey-Predator Model with Age-Structured Growth in Prey and Predation of Beddington-DeAngelis Type with Reliance on Alternative Food

We perform a detailed analysis of the behaviour of a non-autonomous prey-predator model where age-based growth with age discriminatory harvesting in prey and predator's reliance upon alternative food in the absence of that particular prey are considered. We begin by deriving certain sufficient conditions for permanence and positive invariance and then proceed to construct a Lyapunov function to derive some constraints for global attractivity. With the help of continuation theorem, we arrive at the best fit criterion to prove the occurrence of a positive periodic solution. Moreover, using Arzela-Ascoli theorem, we formulate a proof for a unique positive solution to be almost periodic, and we carry out numerical simulation to verify the analytical findings. With the aid of graphs and tables, we show the nature of the prey-predator system in response to the alternative food and delays.