Implementation of PINN model for solving Rosenzweig–MacArthur prey–predator model

This paper presents an approach for solving and optimizing a predator–prey model in which the prey population exhibits logistic growth in the absence of predators. The system is perturbed by selective harvesting. The positivity of solutions is examined, and the existence of multiple equilibrium points is established. The stability of the system is analyzed in relation to these equilibria and their locations. An optimal solution of the model is obtained using a Physics-Informed Neural Network (PINN), where the neural network functions as a deep learning framework. Here, “optimal solution” refers to the conventional minimization of a system-defined objective function and should not be interpreted as biological or ecological optimality. The novelty of this study lies in the incorporation of an additional food term into the predator–prey model and the application of PINNs to solve this modified system. Specifically, we investigate a Rosenzweig–MacArthur model with harvesting and supplementary food (RMHSF). Furthermore, the feasibility and effectiveness of the PINN approach are demonstrated through numerical experiments, with validation performed using datasets and computational implementations in Maple and Python.