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

Cite this article as:

Korotkov A. G., Osipov G. V. Sequential activity in neuronal ensembles with excitatory couplings. Izvestiya VUZ. Applied Nonlinear Dynamics, 2013, vol. 21, iss. 5, pp. 92-107. DOI:


Sequential activity in neuronal ensembles with excitatory couplings

Korotkov Aleksandr Gennadevich, 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"

A new model of neurons like elements is suggested in the paper. The model is based on the generalized Lottka–Volterra model with excitatory coupling. The study is motivated by the fact that the excitatory couplings are the dominating type of interactions between neurons in the human brain. It is shown in the paper that there are two regimes exist in such ensemble of oscillators in dependence on the coupling between the elements: the regime with stable heteroclinical cycle and the regime with stable limit cycle.

Key words: 

1. Rabinovich M.I., Varona P., Selverston A.I., and Abarbanel H.D.I. Dynamical principles in neuroscience // Review of modern physics. 2006. Vol. 78. 1213. 2. 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. 3. 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 // Neural comput. 2004. Vol. 16. P. 999. 4. Levi R., Varona P., Arshavsky Y.I., Rabinovich M.I., and Selverstone A.I. Dual sensory-motor function for a molluskan statocyst network // Neurophysiol J. 2004. Vol. 91. P. 336. 5. Guckenheimer John, and Holmes Philip. Structurally stable heteroclinic cycles // Math. Proc. Camb. Phil. Soc. 1988. Vol. 103. P. 18. 6. Emily Stone, and Philip Holmes. Random perturbations of heteroclinic attractors // SIAM Journal on Applied Mathematics. 1990. Vol. 50, No 3. P. 726. 7. Postlethwaite Claire M., and Dawes Jonathan H.P. Resonance bifurcations from robust homoclinic cycles // Nonlinearity. 2010. Vol. 23. P. 621. 8. Driesse Ramon, and Ale Jan Homburg. Resonance bifurcation from homoclinic cycles // Differential Equations. 2009. Vol. 246. P. 2681. 9. Seliger P., Tsimring L.S., and Rabinovich M.I. Dynamics-based sequential memory: Winnerless competition of patterns // Physical Review E. 2003. Vol. 67. 011905. 10. Afraimovich V.S., Rabinovich M.I., and Varona P. Heteroclinic contours in neural ensembles and the winnerless competition principle // Int. J. of Bifurcation and Chaos. 2004. Vol. 14, No 4. 11. Afraimovich V.S., Zhigulin V.P., and Rabinovich M.I. On the origin of reproducible sequential activity in neural circuits // Chaos. 2004. Vol. 14, No 4. 12. Rabinovich M., Volkovskii A., Lecanda P., Huerta R., Abarbanel H.D.I., and Laurent G. Dynamical encoding by networks of competing neuron groups: Winnerless competition // Physical review letters. 2001. Vol. 87, No 6. 13. Рабинович М.И., Мюезинолу М.К. Нелинейная динамика мозга: Эмоции и интеллектуальная деятельность // Успехи физических наук. 2010. Vol. 180, No 4. 14. Komarov M.A., Osipov G.V. and Suykens J.A.K. Sequentially activated groups in neural networks // EPL. 2009. Vol. 86. 60006.

Short text (in English):