Medium-Term Prediction of Chaos

We study prediction of chaotic time series when a perfect model is available but the initial condition is measured with uncertainty. A common approach for predicting future data given these circumstances is to apply the model despite the uncertainty. In systems with fold dynamics, we find prediction is improved over this strategy by recognizing this behavior. A systematic study of the Logistic map demonstrates prediction of the most likely trajectory can be extended three time steps. Finally, we discuss application of these ideas to the Rössler attractor.