Mathematical Analysis of the Prey-Predator System with Immigrant Prey Using the Soft Computing Technique

In this paper, a mathematical model for the system of prey-predator with immigrant prey has been analyzed to find an approximate solution for immigrant prey population density, local prey population density, and predator population density. Furthermore, we present a novel soft computing technique named LeNN-WOA-NM algorithm for solving the mathematical model of the prey-predator system with immigrant prey. The proposed algorithm uses a function approximating ability of Legendre polynomials based on Legendre neural networks (LeNNs), global search ability of the whale optimization algorithm (WOA), and a local search mechanism of the Nelder-Mead algorithm. The LeNN-WOA-NM algorithm is applied to study the effect of variations on the growth rate, the force of interaction, and the catching rate of local prey and immigrant prey. The statistical data obtained by the proposed technique establish the effectiveness of the proposed algorithm when compared with techniques in the latest literature. The efficiency of solutions obtained by LeNN-WOA-NM is validated through performance measures including absolute errors, MAD, TIC, and ENSE.