Determining the minimum embedding dimensions of input-output time series data

Input-output dynamical systems are in many ways quite different from the autonomous systems that are usually modeled in dynamical system reconstruction. In this paper we investigate the problem of determining the embedding dimension of such systems from input and output data. A successful embedding is essential if one wishes to model the system, or to design a control law. We propose a variant of the well-known false nearest neighbors method, which we call the method of averaged false nearest neighbors. Our method has a simple interpretation and is easy to implement on a computer. We provide several numerical examples.