Modeling nonlinear systems by using nonlinear autoregressive moving average models

The behavior of two coupled nonlinear oscillators is described by a set of coupled nonlinear differential equations. A mapping technique is applied to these equations to generate nonlinear autoregressive moving average (NARMAX) models that relate the sampled input to the sampled response of the nonlinear coupled systems. In contrast to linear multi-degree-of-freedom systems (MDOF) where the system parameters can be obtained from a single higher order ARMA model, the nonlinear MDOF system requires the evaluation of more than one model in order to obtain the desired information about the physical structure of the system. Furthermore, it is seen that nonlinear effects can cause problems when natural frequencies are very close