Intelligent computing for Mathieu's systems for parameter excitation, vertically driven pendulum and dusty plasma models

In this study, a computational intelligence technique is developed to find the solutions of nonlinear Mathieu system arising in parameter excitation, vertically derive pendulum and dusty plasma studies using the strength of artificial neural networks in the modeling of equation and effective optimization of the error function through bioinspired heuristics based on global search with genetic algorithm and rapid local convergence with interior-point algorithm. The proposed scheme is applied to number of scenarios for Mathieu system to analyze the its dynamics for parameter excitation, oscillatory pendulum and dusty plasma models. The comparison of the proposed solutions with numerical results shows a close match which establishes its correctness. The consistent accuracy of the proposed solver is verified through results of statistics in terms of different performance indices based on mean absolute error, root mean square error and Nash-Sutcliffe efficiency. These solutions greatly enrich stochastic numerical solver for the celebrated Mathieu systems. (C) 2017 Elsevier B.V. All rights reserved.