Sabir, ZulqurnainIsmail, AbasJaber, AhmadKhaled, Houssam El DineUmar, MuhammadSalahshour, Soheil2025-07-152025-07-1520251793-96231793-961510.1142/S17939623255004122-s2.0-105008965250https://doi.org/10.1142/S1793962325500412https://hdl.handle.net/20.500.14517/8047This study presents a novel computational neural networks process for solving the prey-predator mathematical model (PPMM). The dynamical form of the PPMM has two species, prey and predator. The importance of this model is signified due to its oscillatory behavior based on the population of two species, as the population of prey enhances, the predator population reduces, and vice versa. A two-layered radial basis deep neural network is performed by using RB in both layers, 22 and 36 neurons in the hidden layer 1 and 2, while the optimization tests are performed through the Bayesian regularization. An implicit Runge-Kutta is used to obtain the reference data, which is divided into training as 82%, while 9% for both authentication and testing. The correctness of the designed radial basis deep neural networks process is approved through the matching of the outputs, best authentication values calculated as 10(-12) to 10(-13), and insignificant absolute error performances found around 10(-7) to 10(-8). The reliability of the radial basis deep neural network process is observed by using different measures based on regression and error histogram.eninfo:eu-repo/semantics/closedAccessRadial BasisDeep Neural NetworksHidden LayersPrey-PredatorBayesian RegularizationArticleN/AQ3WOS:001512792200001