For citation:
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: 10.18500/0869-6632-2013-21-5-92-107
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Article
UDC:
530.18
Sequential activity in neuronal ensembles with excitatory couplings
Autors:
Korotkov Aleksandr Gennadevich, Lobachevsky State University of Nizhny Novgorod
Osipov Grigorij Vladimirovich, Lobachevsky State University of Nizhny Novgorod
Abstract:
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.
Reference:
- Rabinovich MI, Varona P, Selverston AI, Abarbanel HDI. Dynamical principles in neuroscience. Review of modern physics. 2006;78(4):1213–1265. DOI: 10.1103/REVMODPHYS.78.1213.
- Hahnloser RHR, Kozhevnikov AA, Fee MS. An ultra-sparse code underlies the generation of neural sequences in a songbird. Nature (London). 2002;419(6902):65–70. DOI: 10.1038/nature00974.
- Galan R, Sasche S, Galicia CG, Herz AV. Odor-driven attractor dynamics in the antennal lobe allow for simple and rapid olfactory pattern classification. Neur. Comput. 2004;16(5):999–1012. DOI: 10.1162/089976604773135078.
- Levi R, Varona P, Arshavsky YI, Rabinovich MI, Selverstone AI. Dual sensorymotor function for a molluskan statocyst network. J. Neurophysiol. 2004;91(1):336–345. DOI: 10.1152/jn.00753.2003.
- Guckenheimer J, Holmes P. Structurally stable heteroclinic cycles. Math. Proc. Camb. Phil. Soc. 1988;103:189–192. DOI: 10.1017/S0305004100064732.
- Stone E, Holmes P. Random perturbations of heteroclinic attractors. SIAM Journal on Applied Mathematics. 1990;50(3):726–743. DOI: 10.1137/0150043.
- Postlethwaite CM, Dawes JHP. Resonance bifurcations from robust homoclinic cycles. Nonlinearity. 2010;23(3):621–642. DOI: 10.1088/0951-7715/23/3/011.
- Driesse R, Homburg AJ. Resonance bifurcation from homoclinic cycles. Differential Equations. 2009;246(7):2681–2705. DOI: 10.1016/J.JDE.2009.01.034.
- Seliger P, Tsimring LS, Rabinovich MI. Dynamics-based sequential memory: Winnerless competition of patterns. Physical Review E. 2003;67(1):011905. DOI: 10.1103/PhysRevE.67.011905.
- Afraimovich VS, Rabinovich MI, Varona P. Heteroclinic contours in neural ensembles and the winnerless competition principle. Int. J. of Bifurcation and Chaos. 2004;14(4):1195–1208. DOI: 10.1142/S0218127404009806.
- Afraimovich VS, Zhigulin VP, Rabinovich MI. On the origin of reproducible sequential activity in neural circuits. Chaos. 2004;14(4):1123-1129. DOI: 10.1063/1.1819625.
- Rabinovich M, Volkovskii A, Lecanda P, Huerta R, Abarbanel HDI, Laurent G. Dynamical encoding by networks of competing neuron groups: Winnerless competition. Physical review letters. 2001;87(6):068102. DOI: 10.1103/PhysRevLett.87.068102.
- Rabinovich MI, Muezzinoglu MK. Nonlinear dynamics of the brain: emotion and cognition. Phys. Usp. 2010;53(4):357–372. DOI: 10.3367/UFNr.0180.201004b.0371.
- Komarov MA, Osipov GV, Suykens JAK. Sequentially activated groups in neural networks. EPL. 2009;86(6):60006. DOI: 10.1209/0295-5075/86/60006.
Received:
23.04.2013
Accepted:
09.07.2013
Published:
31.12.2013
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