Application of Chebyshev neural network to solve Van der Pol equations

Abstract

In dynamics, the Van der Pol oscillator is a non-conservative oscillator with non-linear damping. The problems of single-well, double-well and double-hump Van der Pol-Dufing equations are studied in this paper. The Chebyshev Neural Network (ChNN) model will be applied to obtain the numerical solutions of these types of equations for the first time. The hidden layer is eliminated by expanding the input pattern by Chebyshev polynomials which employs a single layer neural network. In order to modify the network parameters and to minimize the computed error function, a feed forward neural network model with error back propagation principle is used. The obtained numerical results form the ChNN model will be compared with the analytical solutions, namely Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM), Differential Transform Method (DTM) and exact. Comparisons of the solutions obtained with existing numerical results show that this method is a capable tool for solving this kind of nonlinear problems.

Master-slave synchronization in the van der Pol and Duffing systems via elastic, dissipative and a combination of both couplings

“…Other application is in artificial intelligence. In fact, the oscillators have shown usefulness to training neural network and recognition of chaotic systems Chaharborj et al (2021), Mall and Chakraverty (2016).…”