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

  • B.Zh. Medetov IETP, Al Farabi Kazakh National University, Kazakhstan, Almaty
  • N. Albanbay IETP, Al Farabi Kazakh National University, Kazakhstan, Almaty
  • K.A. Niyazaliyev IETP, Al Farabi Kazakh National University, Kazakhstan, Almaty

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

1. Cronin J. Mathematical aspects of Hodgkin-Huxley neural theory. – Cambridge University Press, 1987. – 261 p.
2. Hodgkin A.L., Huxley A.F. A quantitative description of membrane current and its application to conduction and excitation in nerve // J. Physiol. -1952. - №117. -P.500-544.
3. FitzHygh R. Impulses and physiological states in theoretical models of nerve membrane // Biophys. J. - 1961. - №1. - P.445-466.
4. Pospischil M. et al. Minimal Hodgkin-Huxley type models for different classes of cortical and thalamic neurons. // Biological cybernetics. – 2008. – Vol. 99, № 4-5. – P.427–441.
5. Rabinovich M. et al. Dynamical principles in neuroscience // Reviews of Modern Physics. – 2006. – Vol. 78, № 4. – P.1213–1265.
6. Binczak S. et al. Experimental study of electrical FitzHugh-Nagumo neurons with modified excitability // Neural Networks. Elsevier. - 2006. - Vol. 19, № 5. - P.684–693.
7. Nagumo J., Arimoto S., Yoshizawa S. An active pulse transmission line simulating nerve axon //Proc. IRE. - 1962. - №50. - P.2061-2070.
8. Binczak S., Kazantsev V.B., Nekorkin V.I., Bilbault J.M. Experimental study of bifurcation in modified Fitzhugh-Nagumo cell // Electron. Lett. – 2003. – V.39. – P. 961-962.
9. Nagumo J., Arimoto S., Yoshizawa S. An active pulse transmission line simulating nerve axon // Proc. IRE. - 1962. - №50. - P.2061-2070.
10. Максимов А.Г., Некоркин В.И. Гетероклинические траектории и фронты сложной формы модели ФитцХью-Нагумо // Математическое моделирование. – 1990. – Т.2, №2. – С.129-142.
11. Nekorkin V.I., Kazantsev V.B., Velarde M.G. Spike-burst and other oscillations in a system composed of two coupled, drastically different elements // The European Physical Journal B – 2000. – Vol. 16, № 1. – P. 147–155.
12. Plant R.E. Bifurcation and resonance in a model for bursting nerve cells // Journal of mathematical biology. – 1981. – Vol. 11, № 1. – P. 15–32.
13. Жанабаев З.Ж., Закс М., Медетов Б.Ж. Генерация сигналов кластером связанных двух автоколебательных систем на границе потери устойчивости равновесия. Теория // Журнал проблем эволюции открытых систем. – Алматы, 2012. –Т.1, вып.14. – С.31-35.
14. Наурзбаева А.Ж., Медетов Б.Ж., Ыскак А.Е. Численное исследование двухчастотного режима генерации сигналов кластером автоколебательных систем //Известия НАН РК, серия физическая. – Алматы, 2013. - №2(288). - С. 134-137.
15. Medetov B., Weiss G., Zhanabaev Zh., Zaks M. Numerically induced bursting in a set of coupled neuronal oscillators // Communications in Nonlinear Science and Numerical Simulation. – 2015. – Vol 20, Issue 3. – P.1090-1098.
16. Патент РК №7-9-2929 Трехрежимный радиотехнический генератор сигналов на основе двух линейно – отрицательно связанных нейронов ФитцХью-Нагумо. Жанабаев З.Ж., Медетов Б.Ж., Албанбай Н., Кожагулов Е.Т. Опубл.30.10.2014.
17. Койшигарин А.С., Медетов Б.Ж., Албанбай Н. Численное исследование влияния шума и флуктуаций на режимы генерации кластером автоколебательных систем. Теория. // Журнал ПЭОС. – 2015. – Т.1, - вып. 17.
18. Медетов Б.Ж., Наурзбаева А.Ж., Албанбай Н., Манапбаева А.Б. Экспериментальное измерение сигналов кластера связанных автоколебательных систем // Журнал ПЭОС. – 2013. – Т.1, вып. 15. - С. 17-23.
19. Наурзбаева А.Ж., Медетов Б.Ж., Есерханулы Е. Схемотехническое моделирование «двухчастотной» бифуркации Хопфа // Известия НАН РК, серия физическая. – 2013. – №2(288). - С. 142-145.
20. Медетов Б.Ж., Албанбай Н., Койшигарин А.С., Ниязалиев К.А. ФитцХью-Нагумо нейрондарынан құралған кластердің шуыл әсерінен «тыныштық» күйден «bursting» режиміне көшуін эксперименталдық зерттеу // Сборник тезисов Междун. конф. молодых ученых «Фараби әлемі», 13-16 апреля, 2015, Алматы. – 2015. – С.421.

References
1. J. Cronin, Mathematical aspects of Hodgkin-Huxley neural theory (Cambridge University Press, 1987). doi.org/10.1017/CBO9780511983955.
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). doi.org/10.1016/j.cnsns.2014.07.004
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
2018-04-03
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, apr. 2018. ISSN 1563-0315. Available at: <http://bph.kaznu.kz/index.php/zhuzhu/article/view/572>. Date accessed: 20 apr. 2018.

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