The Long-Time Behavior of Stochastic Prey-Predator Model with the Hide-and-Escape Effect for Prey and Predation Skill Augmentation for Predator

Abstract

In this paper, a comprehensive investigation was conducted of the stochastic prey-predator model combined with the functional and numerical response of the Holling Type II under the influence of the Hide-and-Escape Effect (HEE) for the prey and Predation Skill Augmentation (PSA) for the predator. Initially, the significance of novel effects was elucidated, along with their formulation and integration into the fundamental model. A comprehensive analysis was performed on the proposed model. Theoretically, it has been proven that there is a unique solution in the positive region, and this solution is a global solution. The permanent and extinct conditions of species were also studied in the model. Numerically, the model was simulated using MATLAB, and the resultant theoretical findings were validated.