Embedding as a modeling problem

Standard approaches to time-delay embedding will often fail to provide an embedding that is useful for many common applications. This happens in particular when there are multiple timescales in the dynamics. We present a modified procedure, non-uniform embedding, which overcomes such problems in many cases. For more complex nonlinear dynamics we introduce variable embedding, where, in a suitable sense, the embedding changes with the state of the system. We show how to implement these procedures by combining embedding and modeling into a single procedure with a single optimization goal. (C) 1998 Elsevier Science B.V.