Analysis of a Holling-type IV stochastic prey-predator system with anti-predatory behavior and Lévy noise

In this paper, we investigate a stochastic prey-predator model with Holling-type IV functional responses, anti-predatory behavior (referring to prey resistance to predator), gestation time delay of prey and Lévy noise. We investigate the existence and uniqueness of global positive solutions through Itô's formulation and Lyapunov's method. We also provide sufficient conditions for the persistence and extinction of prey-predator populations. Additionally, we examine the stability of the system distribution and validate our analytical findings through detailed numerical simulations. Our paper concludes with the implications of our results.