ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


Cite this article as:

Mihajlov A. O., Komarov M. A., Osipov G. V. Sequential switching activity in the ensemble of nonidentical poincare systems ?. Izvestiya VUZ. Applied Nonlinear Dynamics, 2013, vol. 21, iss. 5, pp. 79-91. DOI: https://doi.org/10.18500/0869-6632-2013-21-5-79-91

Language: 
Russian

Sequential switching activity in the ensemble of nonidentical poincare systems ?

Autors: 
Mihajlov Aleksej Olegovich, Federal state budgetary educational institution of higher professional education "Nizhny Novgorod state University named N. And.Lobachevsky"
Komarov Maksim Andreevich, Federal state budgetary educational institution of higher professional education "Nizhny Novgorod state University named N. And.Lobachevsky"
Osipov Grigorij Vladimirovich, Federal state budgetary educational institution of higher professional education "Nizhny Novgorod state University named N. And.Lobachevsky"
Abstract: 

Switching activity in the ensemble of inhibitory coupled Poicare systems is considered. The existence of heteroclinic contour in the phase space at the certain domain of parameter space has shown. Dynamics of the ensemble of non-identical inhibitory and di?usively coupled systems of Poincare is considered. The approximate bifurcation diagrams for all qualitatively di?erent regimes of the network activity have shown. There are areas of the parameter space corresponding to di?erent dynamic regimes, such as multistability, extinction, modulation, bursting and synchronization.

Key words: 
DOI: 
10.18500/0869-6632-2013-21-5-79-91
References: 

1. Komarov M.A., Osipov G.V., Suykens J.A.K. and Rabinovich M.I. Numerical studies of slow rhythms emergence in neural microcircuits: Bifurcations and stability // CHAOS. 2009. Vol. 19. 015107. 2. Galan R., Sasche S., Galicia C.G. and Herz A.V. Odor-driven attractor dynamics in the antennal lobe allow for simple and rapid olfactory pattern classification // Neur. Comput. 2004. Vol. 16. P. 999. 3. Levi R., Varona P., Arshavsky Y.I., Rabinovich M.I. and Selverstone A.I. Dual sensorymotor function for a molluskan statocyst network // J. Neurophysiol. 2004. Vol. 91. P. 336. 4. Rabinovich M.I., Varona P., Selverston A.I. and Abarbanel H.D.I. Dynamical principles in neuroscience // Rev. Mod. Phys. 2006. Vol. 19. 015107. 5. Hahnloser R.H.R., Kozhevnikov A.A. and Fee M.S. An ultra-sparse code underlies the generation of neural sequences in a songbird // Nature (London). 2002. Vol. 419. P. 65. 6. Ashwin P., Burylko O. and Maistrenko Y. Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators // Physica D. 2008. Vol. 237. P. 454. 7. Ashwin P. and Field M. Heteroclinic networks in coupled cell systems // Archive for Rational Mechanics and Analysis. 1999. Vol. 148. P. 107. 8. Seliger P., Tsimring L.S. and Rabinovich M.I. Dynamics-based sequential memory: Winnerless competition of pattern // Phys. Rev. E. 2003. Vol. 67. 011905. 9. Afraimovich V.S., Rabinovich M.I. and Varona P. Heteroclinic contours in neural ensembles and the winnerless competition principle // Int. J. Bif. and Chaos. 2004. Vol. 14. 1195. 10. Afraimovich V.S., Zhigulin V.P. and Rabinovich M.I. On the origin of reproducible sequential activity in neural circuits // CHAOS. 2004. Vol. 14. 1123. 11. Komarov M.A., Osipov G.V. and Suykens J.A.K. Sequentially activated groups in neural networks // Europhys. Lett. 2009. Vol. 86. 60006.

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