Modeling the fear effect on a stochastic prey–predator system with additional food for the predator

Abstract

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.

Dynamics of a Predator‐Prey Population in the Presence of Resource Subsidy under the Influence of Nonlinear Prey Refuge and Fear Effect

“…It involves a parameter k denoting the level of fear to represent the antipredator behaviour of the prey. Some research works have already been done on the ecological system under the influence of predation fear felt by prey species [6][7][8][9][10][11][12][13][14][15][16][17]. Moreover, the impact of fear in a two-species predator-prey model with prey refuge was analyzed by many researchers [11,18,19].…”

The Dynamics of a Tritrophic Leslie-Gower Food-Web System with the Effect of Fear

“…Panday et al [7] investigated the action of fear in a three-species food chain model, where the evolution rate of lower predator is minimized due to the fear's action from a higher predator, and the evolution rate of prey is reduced due to the fear's action from the lower predator. Das and Samanta [8] studied the fear's impact from the predator on prey in case of providing additional food for the predator. Recently, Kumar and Kumari [9] discussed the action of fear on the dynamics of the food chain model having three species.…”

Interrelationships between Prey and Predators and How Predators Choose Their Prey to Maximize Their Utility Functions

“…They used the carrying capacity of prey as the bifurcation parameter. You can find more examples on switching models in [11][12][13][14][15][16]. Recently, Serra [17] discussed a preliminary study on the possible connection between the Lotka-Volterra model and predator-prey utility functions.…”