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Regul. Chaotic Dyn., 2015, Volume 20, Issue 6, Pages 701–715 (Mi rcd39)  

Sequential Dynamics in the Motif of Excitatory Coupled Elements

Alexander G. Korotkova, Alexey O. Kazakovb, Grigory V. Osipova

a Lobachevsky State University of Nizhny Novgorod, pr. Gagarina 23, Nizhny Novgorod, 603950 Russia
b National Research University Higher School of Economics, ul. Bolshaya Pecherskaya 25/12, Nizhny Novgorod, 603155 Russia

Abstract: In this article a new model of motif (small ensemble) of neuron-like elements is proposed. It is built with the use of the generalized Lotka–Volterra model with excitatory couplings. The main motivation for this work comes from the problems of neuroscience where excitatory couplings are proved to be the predominant type of interaction between neurons of the brain. In this paper it is shown that there are two modes depending on the type of coupling between the elements: the mode with a stable heteroclinic cycle and the mode with a stable limit cycle. Our second goal is to examine the chaotic dynamics of the generalized three-dimensional Lotka–Volterra model.

Keywords: Neuronal motifs, Lotka–Volterra model, heteroclinic cycle, period-doubling bifurcation, Feigenbaum scenario, strange attractor, Lyapunov exponents

Funding Agency Grant Number
Russian Science Foundation 14-12-00811
14-11-00693
National Research University Higher School of Economics 11.G34.31.0057
The research for this paper was supported by the following grants: the results from Sections 1–3 were supported by the Russian Science Foundation under Contract No. 14-12-00811, those from Sections 4, 5 were supported by the Russian Science Foundation under Contract No. 14-11-00693, and the results from Section 6, 7 were supported by by the Basic Research Program at the National Research University Higher School of Economics (project 138) in 2015 and by LATNA Laboratory, NRU HSE, RF government grant 11.G34.31.0057.


DOI: https://doi.org/10.1134/S1560354715060064

References: PDF file   HTML file

Bibliographic databases:
MSC: 37G35, 70K05, 70K50, 70K55
Received: 04.09.2015
Accepted:07.10.2015
Language:

Citation: Alexander G. Korotkov, Alexey O. Kazakov, Grigory V. Osipov, “Sequential Dynamics in the Motif of Excitatory Coupled Elements”, Regul. Chaotic Dyn., 20:6 (2015), 701–715

Citation in format AMSBIB
\Bibitem{KorKazOsi15}
\by Alexander G. Korotkov, Alexey O. Kazakov, Grigory V. Osipov
\paper Sequential Dynamics in the Motif of Excitatory Coupled Elements
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 6
\pages 701--715
\mathnet{http://mi.mathnet.ru/rcd39}
\crossref{https://doi.org/10.1134/S1560354715060064}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3431185}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2015RCD....20..701K}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84948982958}


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