Synchronization and Intermittency of Type I in the Oscillator Model of Heart Rhythm
DOI:
https://doi.org/10.12970/2311-052X.2016.04.02.2Keywords:
Oscillator, range of power, flicker-noise spectroscopy, veyvlet-transform, area of synchronization.Abstract
With the help of the truncated equation investigated the intermittent behavior of the oscillator Van der Pol oscillator under periodic external action in the absence and in the presence of noise. A method for determining when reinjection by constructing a singular component of the power spectrum of the signal by the flicker noise spectroscopy.
A procedure for determining the current parameters of the oscillator based on the calculation of the wavelet coefficients of the signal system using fast discrete wavelet transform and application of the differentiation formulas wavelet expansions.
References
Schuster G. Determinate chaos. Introduction /Trans. with Eng - M Mir 1988; 240.
Malinetsky GG, Potapov AB. Nonlinear dynamics and chaos. Basic concepts. Publishing house of the 2nd. M.: KomKniga 2000; 240.
Dubois M, Rubio M, Berge P. Experimental evidence of intermiasttencies associated with a subharmonic bifurcation. Phys Rev Lett 1983; 51: 1446. https://doi.org/10.1103/PhysRevLett.51.1446
Platt N, Spiegel EA, Fresser C. On-off intermittency: a mechanism for bursting. Phys Rev Lett 1993; 70(3): 279. https://doi.org/10.1103/PhysRevLett.70.279
Heagy JF, Platt N, Hammel SM. Characterization of on-off intermittency. Phys Rev E 1994; 49(2): 1140. https://doi.org/10.1103/PhysRevE.49.1140
Pikovsky AS, Osipov GV, Rosenblum MG, Zacs M, Kurths JU. Attractor-repeller collision and eyelet intermittency at the transition to phase synchronization. Phys Rev Lett 1997; 79(1): 47. https://doi.org/10.1103/PhysRevLett.79.47
Lee KJ, Kwak Y, Lim TK. Phase jams near a phase synchronization transition in systems of two coupled chaotic oscillators. Phys Rev Lett 1998; 81(2): 321. https://doi.org/10.1103/PhysRevLett.81.321
Hramov AE, Koronovsky AA, Kurovskaya MK, Boccaletti S. Ring intermittency in coupled chaotic oscillators at the boundary of phase synchronization. Phys Rev Lett 2006; 97: 114107. https://doi.org/10.1103/PhysRevLett.97.114101
Timashev SF. Flicker - noise spectroscopy: The information in chaotic signals. M FIZMATLIT 2007; 248.
Pikovsky AS, Rosenblum MG, Kurths JU. Synchronization: a universal concept in nonlinear sciences, Cambridge University Press, 2001; p. 433.
Kuznetsov AP, Kuznetsov SP, Ryskin NM. Nonlinear vibrations. M FIZMATLIT 2002; 292.
Landa PS. Nonlinear Waves. M LIBROKOM 2010; 552.
Pikovsky AS, Rosenblum MG, Kurths JU. Phase synchronization in regular and chaotic systems. Int J Bifurcation and Chaos 2000; 10(10): 2291. https://doi.org/10.1142/S0218127400001481
Khramov AE, Koronovsky AA, Kurovskaya MK. Two types of phase synchronization systems. Phys Rev E 2007; 3: 036,205.
Berge P, Pomeau Y, Vidal Ch. L'ordre dans le chaos. Hermann, Paris, 1988; p. 351.
Koronovsky AA, Kurovskaya MC, Khramov AE. Distribution of the laminar phases for the intermittency of type I in the presence of noise. Math universities "Applied Nonlinear Dynamics" 2009; 17(5): 43-59.
Anischenko VS, Vadivasova TE, Astakhov VV. Nonlinear dynamics of chaotic and stochastic systems. Fundamentals and Selected Problems / Ed. V.S. Anischenko. - Saratov: Izd Sarat. University Press, 1999; p. 368.
Hirsch JE, Huberman BA, Scalapino DJ. Theory of intermittency. Phys Rev A 1982; 25(1): 519. https://doi.org/10.1103/PhysRevA.25.519
Hirsch JE, Nauenberg M, Scalapino DJ. Phys Lett A 1982; 87: 391. https://doi.org/10.1016/0375-9601(82)90165-7
Crutchfield JP, Farmer JD, Huberman BA. Fluctuation and simple chaotic dynamics. Physic Reports (Review Section of Physics Letters) 1982; 92(2): 45-82. https://doi.org/10.1016/0370-1573(82)90089-8
Kye W-H, Kim C-M. Characteristics relations of type-I intermittency in the presence of noise. Phys Rev E 2000; 62(5): 6304. https://doi.org/10.1103/PhysRevE.62.6304
Jin-Hang C, Myung-Suk K, Young-Jai P, Kim C-M. Experimental observation of the characteristic relations of type-I intermittency in the presence of noise. Phys Rev E 2002; 65(3): 036,222.
Brillindzher D. Time series. Processing of data and theory. M Mir 1980; p. 536.
Timashev SF, Vstovskiy GV. Flicker - noise spectroscopy in the analysis of chaotic time series of dynamic variables and the problem of relations "signal - noise". Electrochemistry 2003; 39: 156-169.
Samarsky AA, Gulin AV. Stability of difference schemes. M Nauka 1973; 415.
Vstovsky GV. Elements of Information Physics - M.: Moscow State Pedagogical University, 2002; 258.
Dzhanahmedov AH, Dyshin OA, Javadov MJ. Synergetics and Fractals in tribology. - Baku: APOSTROFF 2014; 504.
Dremin IM, Ivanov OV, Nechitailo VA. Wavelets and their uses. Successes of physical sciences 2001; 171(5): 465-501.
Blatter K. Wavelet analysis. Basic theory. / Transl. from English. - M .: Technosphere 2006; 272.
Daubechies I. wavelet Ten lectures. Moscow Izhevsk: IKI, 2004; 163.
Mallat S. Multiresolution approximation and wavelets. Trans Amer Math Soc 1989; 315: 69-88.
Dyshin OA. The method of calculating the matrix of sustainable performance in wavelet basis functions of differential operators. Proceedings of the Azerbaijan. Techn. University, t. VII (27), №3, 2008, p. 76-82.
Anishchenko VS, Balanov AG, Janson NB, Igosheva NB, Bordyungov GV. Entrainment between heart rate and weak noninvasive forcing. Int J Bifurc Chaos 2000; 10: 2339-2348. https://doi.org/10.1142/S0218127400001468
Abdullayev NT, Dyshin OA, Dzhabieva AD. Analysis of the instability of the time series of RR in terms of criticality samoorganizovannoy. Abstracts of the International scientific-practical conference "Information technologies and computer engineering", Vinnitsa, Ukraine on May 19-21, 2010; pp. 464-465.
Abdullayev NT, Dyshin OA, Abbaskuliev AS. Evaluation of instability -intervalogramm. Medical Technique 2011; №3 (267): 34-37.
