@misc{HuttBeimGraben, author = {Hutt, Axel and Beim Graben, Peter}, title = {Sequences by metastable attractors: interweaving dynamical systems and experimental data}, series = {Frontiers in applied mathematics and statistics}, volume = {3}, journal = {Frontiers in applied mathematics and statistics}, issn = {2297-4687}, doi = {10.3389/fams.2017.00011}, pages = {14}, abstract = {Metastable attractors and heteroclinic orbits are present in the dynamics of various complex systems. Although their occurrence is well-known, their identification and modeling is a challenging task. The present work reviews briefly the literature and proposes a novel combination of their identification in experimental data and their modeling by dynamical systems. This combination applies recurrence structure analysis permitting the derivation of an optimal symbolic representation of metastable states and their dynamical transitions. To derive heteroclinic sequences of metastable attractors in various experimental conditions, the work introduces a Hausdorff clustering algorithm for symbolic dynamics. The application to brain signals (event-related potentials) utilizing neural field models illustrates the methodology.}, language = {en} } @inproceedings{FedotenkovaBeimGrabenSleighetal., author = {Fedotenkova, Mariia and Beim Graben, Peter and Sleigh, Jamie and Hutt, Axel}, title = {Time-frequency representations as phase space reconstruction in symbolic recurrence structure analysis}, series = {Advances in time series analysis and forecasting, selected contributions from ITISE 2016}, booktitle = {Advances in time series analysis and forecasting, selected contributions from ITISE 2016}, editor = {Rojas, Ignacio and Pomares, Hector and Valenzuela, Olga}, publisher = {Springer}, address = {Cham}, isbn = {978-3-319-55789-2}, doi = {10.1007/978-3-319-55789-2_7}, pages = {89 -- 102}, abstract = {Recurrence structures in univariate time series are challenging to detect. We propose a combination of symbolic and recurrence analysis in order to identify recurrence domains in the signal. This method allows to obtain a symbolic representation of the data. Recurrence analysis produces valid results for multidimensional data, however, in the case of univariate time series one should perform phase space reconstruction first. In this chapter, we propose a new method of phase space reconstruction based on the signal's time-frequency representation and compare it to the delay embedding method. We argue that the proposed method outperforms the delay embedding reconstruction in the case of oscillatory signals. We also propose to use recurrence complexity as a quantitative feature of a signal. We evaluate our method on synthetic data and show its application to experimental EEG signals.}, language = {en} }