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The current research work is related to present the numerical solutions of three-species food chain model (TS-FCM) by exploiting the strength of Meyer wavelet neural networks (MWNNs) along with the global and local search competencies. The particle swarm optimization technique works as a global operator, while the sequential quadratic programming scheme is applied as a local operator for the TS-FCM. The nonlinear TS-FCM is dependent upon three categories, called consistent of prey populations, specialist predator and top predator. The optimization of an error-based fitness function is presented by using the hybrid computing efficiency of the global and local search schemes, which is designed through the differential form of the designed ordinary differential model and its initial conditions. The proposed results of the TS-FCM are calculated through the stochastic numerical techniques and further comparison is performed by the Adams method to check the exactness of the scheme. The absolute error in good ranges is performed, which shows the competency of the proposed solver. Moreover, different statistical procedures have also been used to check the reliability of the proposed stochastic procedure along with forty numbers of independent trials and 10 numbers of neurons.

The purpose of this work is to present the stochastic computing study based on the artificial neural networks (ANNs) along with the scaled conjugate gradient (SCG), ANNs-SCG for solving the predator-prey delay differential system of Holling form-III. The mathematical form of the predator-prey delay differential system of Holling form-III is categorized into prey class, predator category and the recent past effects. Three variations of the predator-prey delay differential system of Holling form-III have been numerical stimulated by using the stochastic ANNs-SCG procedure. The selection of the data to solve the predator-prey delay differential system of Holling form-III is provided as 13%, 12% and 75% for testing, training, and substantiation together with 15 neurons. The correctness and exactness of the stochastic ANNs-SCG method is provided by using the comparison of the obtained and data-based reference solutions. The constancy, authentication, soundness, competence, and precision of the stochastic ANNs-SCG technique is performed through the analysis of the correlation measures, state transitions (STs), regression analysis, correlation, error histograms (EHs) and MSE.