Istituto di Biofisica     
Di Garbo A., Barbi M., Chillemi S. ODEs in complex time domain and time series analysis. In: Proceedings of the 4th experimental chaos conference (Boca Raton, Florida, USA, 6-8 august 1997). Proceedings, pp. 193 - 201. Mingzhou Ding, ... [et al.] (eds.). World Scientific, 1998.
The analytical properties of the solutions of a system of 0DEs in the complex time plane influence the real time dynamical evolution. In particular, the extremes of the real solution can be associatedto the singularities of the solution (in the complex time plane) falling near the real time axis. Moreover, for a twice differentiable stochastic process, the expected value of the number of extremes for unit time can be determined. These two results are used here as starting point to introduce two complementary algorithms to test for time series nonlinearity. They don't require the space reconstruction protocol and ' . seem to work well also for limited data sets.
Subject Chaos
Time series
Complex pole

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