Biomedical subjects
Publications and source records attributed to P-M Binder.
A test for determinism suitable for time series shorter than 100 points is presented, and applied to numerical and observed data. The method exploits the linear d(d(0)) dependence in the expression d(t) approximately d(0)e(lambda t) which describes the growth of small separations between trajectories in chaotic systems.
Limit cycles that arise from discretizing the variable(s) of a nonlinear map are generally found to shadow individual unstable periodic orbits (UPOs) of the corresponding continuous map. In a few cases the discretization cycles can only be explained with other mechanisms, such as the near-occurrence of an UPO, or crossover between two or more UPOs.
We perform two direct determinism tests on the El Niño Southern Oscillation index monthly average series. The results indicate that, for timescales over 1 month, the series does not exhibit determinism, an essential feature of chaos.