Global modeling of the Rössler system from the z-variable

Obtaining a global model from the z-variable of the Rössler system is considered to be difficult because of its spiky structure. In this Letter, a 3D global model from the z-variable is derived in a space spanned by the state variable of the time-series itself and generic functions of the other two state variables. We term this space the Ansatz Space. The procedure consists of two steps. First, models built in the derivative coordinates are obtained. Second, we use the analytical form of the map φ between systems in the original state space and in the differential space to find a class of models in the Ansatz Space. We find eight models in this class which we show to be dynamically equivalent to the original Rössler system. The important attribute of this approach is that we do not need to use any prior knowledge of the dynamical system other than the measured time series data in order to obtain global models from a single time series.  2003 Elsevier B.V. All rights reserved.