ABSTRACT
The Van der Pol–Duffing oscillator equation is a classical nonlinear oscillator, which is a very useful mathematical model for understanding different engineering problems. This equation is widely used to model various physical problems, namely, electrical circuits, electronics, mechanics, etc. This chapter considers single-layer simple orthogonal polynomial–based neural network (SOPNN) and Hermite neural network (HeNN) models to handle unforced and forced Van der Pol–Duffing oscillator equations, respectively. It also considers the Van der Pol–Duffing oscillator equation without periodic force. The Van der Pol–Duffing oscillator equation has been used in various real-life problems. Hu and Wen applied the Duffing oscillator for extracting the features of early mechanical failure signal. The nonlinear Duffing oscillator equation and the Van der Pol–Duffing oscillator equations are difficult to solve analytically. The Van der Pol–Duffing oscillator is a classical example of a self-oscillatory system and is now considered as a very important model to describe a variety of physical systems.
