# Experimental determination of the statistics of the number of bursts in a cluster of auto-oscillatory systems

### Abstract

In the study of a cluster of auto-oscillating systems consisting of two coupled FitzHugh-Nagumo neurons, four signal generation modes were defined: "fast", "slow", "bursting", "rest". It is established that the qualitative transition from one regime to another occurs not only in dependence on the given initial conditions and the parameters of the system, but also because of the influence of noise and fluctuations. In addition, it was found that for a certain range of noise intensity for the same parameter values, the number of bursts generated in bursting mode is finite and not constant. To study the regularity of the distribution of the number of bursts, an experimental setup has been assembled, with the help of which the corresponding statistics were measured automatically. The automation of the experiment was carried out by means of LabVIEW, and data processing and calculation of the distribution of the number of bursts were calculated according to a certain algorithm in the Matlab environment. As a result, it is established that the distribution of bursts is described by an exponential dependence.### References

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2. A.L. Hodgkin and A.F. Huxley, J. Physiol 117, 500-544, (1952).

3. R. FitzHygh, Biophys 1, 445-466, (1961).

4. M. Pospischil at al, Biological cybernetics 99, № 4-5, 427–441, (2008).

5. M. Rabinovich at al. Reviews of Modern Physics 78, 4, 1213–1265, (2006).

6. S. Binczak at al, Neural Networks 19, 5, 684–693, (2006).

7. J. Nagumo, S. Arimoto, and S. Yoshizawa, Proc. IRE 50, 2061-2070, (1962).

8. S. Binczak, V.B. Kazantsev, V.I. Nekorkin, and J.M. Bilbault, Electron. Lett. 39, 961-962, (2003).

9. J. Nagumo, S. Arimoto and S. Yoshizawa, Proc. IRE 50, 2061-2070, (1962).

10. A.G. Maksimov and V.I. Nekorkin, Matematicheskoye modelirovaniye 2, 129-142, (1990). (in Russ).

11. V.I. Nekorkin, V.B. Kazantsev, and M.G. Velarde,The European Physical Journal B 16, 1, 147–155, (2000).

12. R.E. Plant, Journal of mathematical biology 11, 15–32, (1981).

13. Z.Zh. Zhanabayev, M. Zaks, and B.ZH. Medetov, Zhurnal problem evolyutsii otkrytykh sistem 1, 31-35, (2012). (in Russ).

14. А.Zh. Naurzbayeva, B.ZH. Medetov, and A.Ye. Yskak, Izvestiya NAN RK, seriya fizicheskaya 2(288), 134-137, (2013). (in Russ).

15. B. Medetov, G. Weiss, Zh. Zhanabaev and M. Zaks., Communications in Nonlinear Science and Numerical Simulation 20, 3, 1090-1098, (2015).

16. Patent RK №7-9-2929ю Trekhrezhimnyy radiotekhnicheskiy generator signalov na osnove dvukh lineyno – otritsatel'no svyazannykh neyronov FittsKH'yu-Nagumo, Z.Zh. Zhanabayev, B.Zh. Medetov, N. Albanbay i Ye.T. Kozhagulov. Opubl.30.10.2014. (in Russ).

17. A.S. Koyshigarin, B.ZH. Medetov i N. Albanbay, Zhurnal problem evolyutsii otkrytykh sistem 17, 1, (2015) (in Russ).

18. B.Zh. Medetov, A.Zh. Naurzbayeva, N. Albanbay, and A.B. Manapbayeva, Zhurnal problem evolyutsii otkrytykh sistem 1, 15, 17-23, (2013). (in Russ).

19. A.Zh. Naurzbaeva, B.Zh. Medetov, and E. Yeserhanuly, Izvestiya NAS RK, series physical 2, 288, 142-145, (2013). (in Russ).

20. B.ZH. Medetov, N. Albanbay, A.S. Koyshigarin, and K.A. Niyazaliyev, Book abstract of the Intern. Conf. «Farabi alemi», (13-16 April, 2015, Almaty), 421. (in Russ).

Published

2017-09-25

How to Cite

MEDETOV, B.Zh.; ALBANBAY, N.; NIYAZALIYEV, K.A..
Experimental determination of the statistics of the number of bursts in a cluster of auto-oscillatory systems.

**Recent Contributions to Physics (Rec.Contr.Phys.)**, [S.l.], v. 62, n. 3, p. 106-113, sep. 2017. ISSN 2663-2276. Available at: <https://bph.kaznu.kz/index.php/zhuzhu/article/view/901>. Date accessed: 24 oct. 2020.
Section

Condensed Matter Physics and Materials Science Problems. NanoScience