Coupled nonlinear stochastic integral equations in the general form of the predator-prey model

Abstract

This article explores the stochastic predator-prey model. This model offers a probabilistic framework for understanding the dynamics of interacting species. The stochastic predator-prey model is a practical tool for predicting the intricate balance of survival between predators and their prey in the face of nature's unpredictability. This study introduces a new measure of noncompactness and applies it to investigate solutions in nonlinear stochastic equations. Additionally, we present a numerical method using block pulse functions and demonstrate its convergence through the new measure of noncompactness for solving the system of stochastic integrals. Finally, the proposed method is employed to solve a numerical example.