Gudermannian neural network procedure for the nonlinear prey-predator dynamical system

Abstract

The present study performs the design of a novel Gudermannian neural networks (GNNs) for the nonlinear dynamics of prey-predator system (NDPPS). The process of GNNs is applied using the global and local search approaches named as genetic algorithm and interior-point algorithms, i.e., GNNs-GA-IPA. An error-based merit function is constructed using the NDPPS and its initial conditions and then optimized by the hybrid of GA-IPA. Six cases of the NDPPS using the variable coefficients have been presented and the correctness is observed through the overlapping of the obtained and Runge-Kutta reference results. The results of the NDPPS have been performed between 0 and 5 using the step size 0.02. The graph of absolute error are performed around 10 ⁻⁰⁶ to 10 ⁻⁰⁸ to check the consistency of the proposed GNNs-GA-IPA. The statistical analysis based minimum, median and semi-interquartile ranges have been performed for both predator and prey dynamics of the model. Moreover, the investigations through the statistical operators are performed to validate the reliability of the obtained outcomes based on multiple trials.