Intelligent computing for Duffing-Harmonic oscillator equation via the bio-evolutionary optimization algorithm

Abstract

This paper presents a bio-evolutionary metaheuristic approach to study the harmonically oscillating behavior of the Duffing equation. The proposed methodology is an amalgamation of the artificial neural network with the firefly algorithm. A novelty in the activation of neurons of artificial neural network is described using the cosine function with the angular frequency. Chronologically, artificial neural network approximates discretizes the nonlinear functions of the governing problem, which then undergoes an optimization process by the firefly algorithm that then later generates the effective values of the unknown parameters. Generally, the algorithm and implementation of the scheme are assimilated by considering an application of Duffing-harmonic oscillator. Some error measurements, in order to discuss the convergence and accuracy of the scheme, are also visualized through tables and graphs. An effective optimized relationship between the angular frequency and amplitude is derived and its results are depicted in a tabular form. The comparison of the proposed methodology is also deliberated by homotopy perturbation method. Moreover, the geometrical illustration of the trajectories of the dynamic system is also added in the phase plane for different values of amplitude and angular frequency.

Atomic Fisher information and entanglement forecasting for quantum system based on artificial neural network and time series model

“…[ 24 ] The errors work to evaluate the derivatives of the error function with respect to the weights, which can then be adjusted. [ 25,26,27 ]…”

Cognitive Neural Computation Modeling of Human Brain Information Storage and Extraction Based on Intelligent Computing

“…A novel feature of ANN activation is the use of cosine functions and some error measurements are given in tables and graphs to discuss the convergence and accuracy of the scheme. Te trajectories of the dynamical systems are also complemented with geometrical descriptions of the amplitude and angular frequency for diferent values of the phase level [5]. Saleem Durai and Sundaresan proposed a new intelligent computing framework that uses fuzzy machine clustering with extreme learning and formulates adaptive and cognitive energy and power allocation rules based on kernels [6].…”

Solution to a Damped Duffing Equation Using He’s Frequency Approach

“…Solution methods for nonlinear oscillators include the G/G method, modified mapping method and the extended mapping method, elliptic expansion method, modified (G/ G)-expansion method, dynamical systems approach, the modified trigonometric function series method, generalized (G/G)-expansion method, tanh method, and the sn-ns method, among others [1][2][3][4][5][6][7][8][9][10].…”