A Recurrent Artificial Neural Network Model of Duffing's Equation without Training
Andrew J. Meade, Jr. and Rafael Moreno,
Submitted to International Journal of Smart Engineering System Design, 1996.

Keywords:: recurrent artificial neural networks, neural computation, differential equations, chaos, network training.

Abstract: A method is developed for constructing recurrent artificial neural networks to model physical systems. The construction requires imposing certain constraints on the values of the input, bias, and output weights. The attribution of certain roles to each of these parameters allows for mapping a polynomial approximation into an artificial neural network architecture. Attention is focused on a second-order nonlinear ordinary differential equation, which governs the well known Duffing's oscillator. The nonlinear ordinary differential equation is modelled by the recurrent artificial neural network architecture in conjunction with the popular hyperbolic tangent transfer function. Moreover, this approach is shown to be capable of incorporating other smooth neuron transfer functions, as long as they can be described by a Taylor series expansion. Numerical examples are presented illustrating the accuracy and utility of the method.

This work is supported under NASA grant NAG 9-719 and ONR grant N00014-95-1-0741.

29 pages.