Detecting chaos with neural networks

Predictions of the future values of a time series can be used to try to distinguish chaotic from noisy signals. We show that neurally inspired networks provide a powerful tool for this task, in that they can reliably distinguish between predictable, chaotic and noisy records. We have used these neural networks to analyse the 'standard' time series of measles and chickenpox cases in New York City. Applied to these real time series these new methods perform as well as a recently developed technique. We also employed feedforward and recurrent networks to analyse several sets of artificially generated data and found that they exhibit advantages over other recent techniques. These networks were able to generalize the rules governing the generation of the time series from very few data points and could also forecast series generated by non-stationary dynamics.