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    Boris Bezrychko

    Astrahanskaya st. 83, Saratov, 410012, Russia
    Saratov State University named after N. G. Chernyshevsky


    Ishbulatov J. M., Karavaev A. S., Ponomarenko V. I., Kiselev A. R., Sergeev S. A., Seleznev Y. P., Bezrychko B. P., Prokhorov M. D.
    We propose an original mathematical model for the human cardiovascular system. The model simulates the heart rate, autonomous control of heart, arterial pressure and cardiorespiratory interaction. Taking into account the self-excited autonomic control allowed us to reproduce the experimentally observed effects of phase synchronization between the control elements. The consistency of the proposed model is validated by quantitative and qualitative reproduction of spectral and statistical characteristics of real data from healthy subjects. Within physiological values of the parameters the model demonstrates chaotic dynamics and reproduces spontaneous interchange between the intervals of spontaneous and nonspontaneous behavior.
    Keywords: mathematical model, synchronization, cardiovascular system, dynamic chaos, time delay system
    Citation: Ishbulatov J. M., Karavaev A. S., Ponomarenko V. I., Kiselev A. R., Sergeev S. A., Seleznev Y. P., Bezrychko B. P., Prokhorov M. D.,  Phase synchronization of elements of autonomic control in mathematical model of cardiovascular system, Rus. J. Nonlin. Dyn., 2017, Vol. 13, No. 3, pp.  381-397
    Kornilov M. V., Sysoev I. V., Bezrychko B. P.
    The detection of coupling presence and direction between various systems using their time series is a common task in many areas of knowledge. One of the approaches used to solve it is nonlinear Granger causality method. It is based on the construction of forecasting models, so its efficiency defends on selection of model parameters. Two parameters are important for modeling signals with a main time scales: lag that is used for state vector reconstruction and prediction length.
    In this paper, we propose two criteria for evaluating performance of the method of nonlinear Granger causality. These criteria allow to select lag and prediction length, that provide the best sensitivity and specificity. Sensitivity determines the weakest coupling method can detect, and specificity refers to the ability to avoid false positive results. As a result of the criteria application to several etalon unidirectionally coupled systems, practical recommendations for the selection of the model parameters (lag and prediction length) were formulated.
    Keywords: search for coupling, Granger causality, modeling from time series
    Citation: Kornilov M. V., Sysoev I. V., Bezrychko B. P.,  Optimal selection of parameters of the forecasting models used for the nonlinear Granger causality method in application to the signals with a main time scales, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 3, pp.  279-295

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