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Koloskova A. D. Determining of the intermittent phase synchronization degree from neurophysiological. *Izvestiya VUZ. Applied Nonlinear Dynamics*, 2017, vol. 25, iss. 5, pp. 26-34. DOI: 10.18500/0869-6632-2017-5-26-34

# Determining of the intermittent phase synchronization degree from neurophysiological

In this paper we present the results of investigation of intermittent phase synchronization in a real neurophysiological system. This phenomenon is observed in different systems as well as near the boundaries of various types of chaotic synchronization. In the case of electroencephalogram (EEG) of the brain, chosen as a system under study, just the intermittent phase synchronization can indicate the existence and development of pathologies, for example, the presence of epileptic seizures. Creation and introduction of the newest methods for the analysis of various types of brain dynamics are one of the most popular and actively developing spheres in neurophysiology. EEG signals taken from the brain of a special laboratory WAG/Rij rat, which genetically predisposed to epileptic seizures, were observed. The rat is studied in two states: under the influence of the drug clonidine (results in the intensification of epileptic seizures during the first 6-12 hours, but does not affect the duration of spike-wave discharges) and without it. To estimate the degree of intermittent behavior the method based on the calculation of zero conditional Lyapunov exponent was chosen. The relation of conditional Lyapunov exponents for the phase difference of two different channels of the animal’s brain in the case of the drug influence and in their absence is found. Plots of the dependence of the investigated quantity on the number of the spike-wave discharge are constructed. It was found that the spike-wave discharges are better synchronized under the influence of the drug. The results of this work can find direct application in medicine for diagnostics and detection of diseases associated with pathological activity of the brain.

- Janson N.B., Balanov A.G., Anishchenko V.S., McClintock P.V.E. Phase synchronization between several interacting processes from univariate data. Phys. Rev. Lett. 2001. Vol. 86 (9). Pp. 1749–1752.
- Bob P., Palus M., Susta M., Glaslova K. EEG phase synchronization in patients with paranoid schizophrenia. Neuroscience Letters. 2008. Vol. 447. Pp. 73–77.
- Anischenko V.S., Postnov D.E. Effect of locking of the base frequency of chaotic oscillations. Synchronization of strange attractors. Soviet Technical Physics Letters. 1988. Vol. 14 (6). Pp. 569–573 (in Rissian).
- Rosenblum M.G., Pikovsky A.S., Kurths J. Phase synchronization of chaotic oscillators. Phys. Rev. Lett. 1996. Vol. 76 (11). Pp. 1804–1807.
- Pikovsky A.S., Osipov G.V., Rosenblum M.G., Zaks M., Kurths J. Attractor-repeller collision and Eyelet intermittency at the transition to phase synchronization. Phys. Rev. Lett. 1997. Vol. 79 (1). Pp. 47–50.
- Hramov A.E., Koronovskii A.A., Kurovskaya M.K., Boccaletti S. Ring intermittency in coupled chaotic oscillators at the boundary of phase synchronization. Phys. Rev. Lett. 2006. Vol. 97. 114101.
- Hramov A.E., Koronovskii A.A, Kurovskaya M.K., Ovchinnikov A.A., Boccaletti S. Length distribution of laminar phases for type-I intermittency in the presence of noise. Phys. Rev. 2007. Vol. E76. 026206.
- Kurovskaya M.K. Distribution of laminar phases at Eyelet-type intermittency. Technical Physics Letters. 2008. Vol. 34 (12). Pp. 1063–1065.
- Hramov A.E., Koronovskii A.A., Kurovskaya M.K. Zero Lyapunov exponent in the vicinity of the saddle-node bifurcation point in the presence of noise. Phys. Rev. E. 2008. Vol. 78. 036212.
- Moskalenko O.I., Koronovskii A.A., Hramov A.E. Lyapunov exponent corresponding to enslaved phase dynamics: Estimation from time series. Phys. Rev. E. 2015. Vol. 92. P. 012913.
- Moskalenko O.I., Koronovskii A.A., Hramov A.E., Zhuravlev M.O. Estimate of the degree of synchronization in the intermittent phase synchronization regime from a time series: Model systems and neurophysiological data. JETP Letters. 2016. Vol. 103 (8). Pp. 539–543.
- Moskalenko O.I., Pavlov A.S. A method of evaluating a zero conditional Lyapunov exponent from time series. Technical Physics Letters. 2014. Vol. 40 (6). Pp. 546–548.
- Koloskova A.D., Moskalenko O.I. Determining the degree of synchronism for intermittent phase synchronization in human electroencephalography data. Technical Physics Letters. 2017. Vol. 43 (5). Pp. 499–502.
- Moskalenko O.I., Koloskova A.D., Zhuravlev M.O., Koronovskii A.A., Hramov A.E. Intermittent phase synchronization in human epileptic brain. Proc. SPIE. 2017. Vol. 10063. 1006316.
- Coenen A.M., van Luijelaar E.L. The Wag/Rij rat model for absence epilepsy: Age and sex factors. Epilepsy Res. 1987. Vol. 1 (5). Pp. 297–301.
- Hramov A.E., Koronovskii A.A., Makarov V.A., Pavlov A.N., Sitnikova E.Yu. Wavelets in Neuroscience. Springer: Heidelberg New York, Dordrecht London, 2015.
- Sitnikova E.Yu., Hramov A.E., Koronovskii A.A., van Luijtelaar G. Sleep spindles and spike-wave discharges in EEG: Their generic features, similarities and distinctions disclosed with Fourier transform and continuous wavelet analysis. Journal of Neuroscience Methods. 2009. Vol. 180. Pp. 304–316.
- van Luijtelaar G., Hramov A.E., Sitnikova E.Yu., Koronovskii A.A. Spike-wave discharges in WAG/Rij rats are preceded by delta and theta precursor activity in cortex and thalamus. Clinical Neurophysiology. 2011. Vol. 122. Pp. 687–695.
- Hramov A.E., Koronovskii A.A. An approach to chaotic synchronization. Chaos. 2004. Vol. 14 (3). Pp. 603–610.

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