Влияние электрической связи на динамику ансамбля нейроноподобных элементов с синаптическими тормозящими связями

Известия высших учебных заведений. Прикладная нелинейная динамика. 2018. Т. 26. № 5. С. 101–112.

Kazakov A., Леванова Т. А., Коротков А. Г., Осипов Г. В.

The phenomenological model of an ensemble of three neurons which are coupled by
chemical (synaptic) and electrical couplings is studies. A neuron is modeled by the oscillator of van
der Pol. The aim of work is a study of the influence of coupling’s strength and frequency detuning
between elements at regime of sequential activity that is observed in the ensemble of neuron-like
elements with chemical inhibitory couplings. Method. The research is made with usage of
analytical methods of nonlinear dynamics and computer modeling. Results. The study showed
that the introduction of arbitrarily small electrical coupling into ensemble of Van der Pol oscillators
with chemical synaptic inhibitory couplings leads to the destruction of a stable heteroclinic
contour between saddle limit cycles. We showed also that nonidentity of elements (while
electrical couplings is absent) does not lead to the destruction of heteroclinic contour, what, in
general, is not typical for such systems. Discussion. We suggest to consider studied ensemble
of elements as phenomenological model of neuronal network. Such approach has advantages:
it is possible to study low-dimensional neuronal models and reproduce the main effects that are
observed in more complex models, for example, in biologically realistic model of Hodgkin-
Huxley and in real experiments also.
 

Keywords: neurons, нейроны, heteroclinic cycle, Duffing–van der Pol oscillator, chemical coupling, electrical coupling, химическая связь, электрическая связь, осциллятор ван дер Поля, гетероклинический контур

Publication based on the results of: Topology and chaos in the dynamics of systems, foliations, and deformations of Lie algebras (2018)