  A hybrid approach, incorporating concepts of nonlinear dynamics in artificial
neural networks (ANN), is proposed to model time series generated by complex
dynamic systems. We introduce well known features used in the study of dynamic
systems - time delay $\tau$ and embedding dimension $d$ - for ANN modelling of
time series. These features provide a theoretical basis for selecting the
optimal size for the number of neurons in the input layer. The main outcome for
the number of neurons in the input layer. The main outcome of the new approach
for such problems is that to a large extent it defines the ANN architecture and
leads to better predictions. We illustrate our method by considering computer
generated periodic and chaotic time series. The ANN model developed gave
excellent quality of fit for the training and test sets as well as for
iterative dynamic predictions for future values of the two time series.
Further, computer experiments were conducted by introducing Gaussian noise of
various degrees in the two time series, to simulate real world effects. We find
rather surprising results that upto a limit introduction of noise leads to a
smaller network with good generalizing capability.
