Determining periodic orbits via nonlinear filtering and recurrence spectra in the presence of noise

Sebastian Oberst, Steffen Marburg & Norbert Hoffmann
In nonlinear dynamical systems the determination of stable and unstable periodic orbits as part of phase space prediction is problematic in particular if perturbed by noise. Fourier spectra of the time series or its autocorrelation function have shown to be of little use if the dynamic process is not strictly wide-sense stationary or if it is nonlinear. To locate unstable periodic orbits of a chaotic attractor in phase space the least stable eigenvalue can be...
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