Chaotic signal processing via unstable cycle extraction

The existence of a countable infinity of unstable periodic orbits is one of the main features of chaotic behavior and strange attractors. We exploit this property from the signal processing point of view. Processing of a chaotic time series measured from some unknown process involves the reconstruction of system dynamics, uncovering the unstable periodic orbits embedded in the attractor and the calculation of eigenvalues. Such a characterisation obtained via numerical data processing is further used for the suppression of chaos, i.e. control in terms of stabilisation of chosen orbit