LAUSR

In the present work we have studied a prey–predator model with logistic growth of the prey in the absence of the predator. We have also considered the fear effect and have investigated the impact of fear of the predator on prey when the predator is provided additional food. Functional responses of the predator towards prey and additional food are derived in this text. Death rates of both prey and predator have been considered as stochastic parameters due to the effect of the fluctuating environment. Existence and uniqueness, boundedness and uniform continuity of the global positive solution of the proposed model have been established. The conditions for extinction and persistence of the system have been derived. In the investigation, it is found that environmental noise plays a vital role in extinction as well as in persistence. Our analytical derivations are justified through numerical simulations which show the reliability of the model from the ecological point of view. We have also investigated the impact of intense fear as well as the absence of fear on this model by numerical simulation. Several interesting numerical results have been obtained based on different fear functions.