Abstract:
On the basis of test data self-similar rate of curves of the instantaneous cardiac rhythm is shown. Within a model of multi-fractal dynamics received equations that describe the piecewise linear trend of instant heart rate. It is proposed classification of types of its dynamics as a function of the fractal dimension of D of the curve of heart rate on the basis of equations. In the field of values of D near bifurcation points of Db is the bifurcation phenomena having jumps of speed of a piecewise linear trend of instant heart rate.
Citation:
A. N. Kudinov, D. Y. Lebedev, V. P. Tsvetkov, I. V. Tsvetkov, “Mathematical model of multi-fractal dynamics and analysis of heart rate”, Mat. Model., 26:10 (2014), 127–136; Math. Models Comput. Simul., 7:3 (2015), 214–221
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Evaristo R.M., Batista A.M., Viana R.L., Iarosz K.C., Szezech Jr. Jose D., de Godoy M.F., “Mathematical Model With Autoregressive Process For Electrocardiogram Signals”, Commun. Nonlinear Sci. Numer. Simul., 57 (2018), 415–421
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V.P. Tsvetkov, S.A. Mikheyev, I.V. Tsvetkov, “Fractal phase space and fractal entropy of instantaneous cardiac rhythm”, Chaos, Solitons & Fractals, 108 (2018), 71
A.N. Kudinov, S.A. Mikheev, V.P. Tsvetkov, I.V. Tsvetkov, Proceedings of the International Conference “Mathematical Biology and Bioinformatics”, 7, Proceedings of the International Conference “Mathematical Biology and Bioinformatics”, 2018
A. P. Ivanov, A. N. Kudinov, D. Yu. Lebedev, S. A. Mikheev, V. P. Tsvetkov, I. V. Tsvetkov, “Katastrofy mgnovennogo serdechnogo ritma v modeli multifraktalnoi dinamiki i po dannym kholterovskogo monitorirovaniya”, Matem. modelirovanie, 29:5 (2017), 73–84
S. A. Mikheev, V. N. Ryzhikov, V. P. Tsvetkov, I. V. Tsvetkov, “Vychislenie parametrov mgnovennogo serdechnogo ritma v modeli multifraktalnoi dinamiki regulyarizovannym metodom Nyutona”, Matem. modelirovanie, 29:12 (2017), 147–156
A. P. Ivanov, A. N. Kudinov, D. Yu. Lebedev, S. A. Mikheev, V. P. Tsvetkov, I. V. Tsvetkov, “Bifurkatsionnye katastrofy mgnovennogo serdechnogo ritma v modeli multifraktalnoi dinamiki”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2016, no. 1, 63–73
Smetanin V., Tsvetkov I., Nasonov A., 5Th International Scientific Conference Integration, Partnership and Innovation in Construction Science and Education, Matec Web of Conferences, 86, ed. Andreev V., E D P Sciences, 2016
A. P. Ivanov, A. N. Kudinov, D. Y. Lebedev, V. P. Tsvetkov, I. V. Tsvetkov, “Analysis of instantaneous cardiac rhythm in a model multi-fractal dynamics based on Holter monitoring”, Math. Models Comput. Simul., 8:1 (2016), 7–18
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