Predicting chaotic time series with a partial model.
Methods for forecasting time series are a critical aspect of the understanding and control of complex networks. When the model of the network is unknown, nonparametric methods for prediction have been developed, based on concepts of attractor reconstruction pioneered by Takens and others. In this Rapid Communication we consider how to make use of a subset of the system equations, if they are known, to improve the predictive capability of forecasting methods. A counterintuitive implication of the results is that knowledge of the evolution equation of even one variable, if known, can improve forecasting of all variables. The method is illustrated on data from the Lorenz attractor and from a small network with chaotic dynamics.
Department of Electrical and Computer Engineering and Department of Mathematical Sciences, George Mason University, Fairfax, Virginia 22030, USA.
Franz
F
Hamilton
Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802, USA.
Tyrus
T
Berry
Department of Electrical and Computer Engineering and Department of Mathematical Sciences, George Mason University, Fairfax, Virginia 22030, USA.
Timothy
T
Sauer