On the stochastic observation for the nonlinear system of the emigration and migration effects via artificial neural networks

Abstract

Abstract The aim of this work is to solve a mathematical model based on the migration and emigration effects. The designed mathematical model shows one of the forms of prey-predator. The migration factor represents a step function for both normal and individuals that is restrictions or movement of people. The numerical solutions of the designed model are presented using the stochastic computational schemes based on the artificial neural networks (ANNs) together with the Levenberg-Marquardt back propagation (LMB), i.e., ANNs-LMB for solving the model based on the migration and emigration effects. Three different cases have been performed to solve the model based on the migration and emigration effects with the ANNs-LMB solver in terms of authentication, training, sample statistics and testing. The selection of the data is chosen as 80%, 10%, 10% for training, testing and authentication, respectively. The numerical results through the ANNs-LMB of the model based on the migration and emigration effects will be compared with the Runge-Kutta method. The results of the model based on the migration and emigration effects using the ANNs-LMB are provided to reduce the mean square error (MSE). For the capability and efficiency of the proposed ANNs-LMB, the numerical results are provided using the correlation, error histograms, regression and MSE.