Characterization of complex interdependencies of oscillatory processes from data with extended phase dynamics methods

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This is a continuation of the Project B3 with the overall aim to exploit recent achievements of nonlinear dynamics in order to advance techniques of multivariate analysis of neural data.The key point of the project is reconstruction of the equations of the phase dynamics, which is performed in an invariant way, i.e. independently of the observables used. The obtained equations yield a complete description of interaction between nonlinear neural oscillators. The main task of the project is to extend the techniques, developed in the first stage of the Project, to cover more complex setups, and to apply them to neural activity involved incognition.The extension will be pursued in the following directions: (i) incorporation of new statistical approaches, like kernel function estimation, into the existing framework with the aim to obtain reliable model reconstruction from very short and inhomogeneous data sets; (ii) extension of the method to cover noise-induced oscillations by means of effective phase dynamics descripfion of such systems; (iii) extension for the case of many interacfing oscillating units, with especial emphasis on the effects of non-painwise interaction; (iv) search for the effects of nonlinearity in interaction, what is yet unexplored even on the modeling level.