Regular and Chaotic Dynamics

, Volume 20, Issue 6, pp 701–715 | Cite as

Sequential dynamics in the motif of excitatory coupled elements

  • Alexander G. Korotkov
  • Alexey O. Kazakov
  • Grigory V. Osipov
Article

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 

MSC2010 numbers

37G35 70K05 70K50 70K55 

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  • Alexander G. Korotkov
    • 1
  • Alexey O. Kazakov
    • 2
  • Grigory V. Osipov
    • 1
  1. 1.Lobachevsky State University of Nizhny NovgorodNizhny NovgorodRussia
  2. 2.National Research University Higher School of EconomicsNizhny NovgorodRussia

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