The impact of electrical couplings on the dynamics of the ensemble of inhibitory coupled neuron-like elements
Cite this article as:
Levanova T. A., Kazakov A. O., Korotkov А. ., Osipov G. V. The impact of electrical couplings on the dynamics of the ensemble of inhibitory coupled neuron-like elements. Izvestiya VUZ. Applied Nonlinear Dynamics, 2018, vol. 26, iss. 5, pp. 101-112. DOI: https://doi.org/10.18500/0869-6632-2018-26-5-101-112
Topic. The phenomenological model of ensemble of three neurons coupled by chemical (synaptic) and electrical couplings is studied. Single neuron is modeled by van der Pol oscillator. Aim of work is to study of influence of coupling strength and frequency detuning between elements in the case of regime of sequential activity that is observed in ensemble of neuronlike elements with chemical inhibitory couplings. Method. The research is made with usage of analytical methods of nonlinear dynamics and computer modeling. Results. It was shown that adding of arbitrarily small electrical coupling to ensemble of van der Pol oscillators with chemical synaptic inhibitory couplings leads to the destruction of a stable heteroclinic contour between saddle limit cycles. It was also shown that nonidentity of elements (while electrical couplings are absent) do not lead to destruction of heteroclinic contour. This situation, in general, is not typical for such systems. Discussion. We suggest to consider the ensemble of elements as phenomenological model of neuronal network. Such approach has the following advantage: 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 also in real experiments.
BibTeX
author = {T. A. Levanova and A. O. Kazakov and А G. Korotkov and G. V. Osipov },
title = {The impact of electrical couplings on the dynamics of the ensemble of inhibitory coupled neuron-like elements},
year = {2018},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {26},number = {5},
url = {https://old-andjournal.sgu.ru/en/articles/the-impact-of-electrical-couplings-on-the-dynamics-of-the-ensemble-of-inhibitory-coupled},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2018-26-5-101-112},pages = {101--112},issn = {0869-6632},
keywords = {Neuron,chemical coupling,electrical coupling,Van der Pol oscillator,heteroclinic contour},
abstract = {Topic. The phenomenological model of ensemble of three neurons coupled by chemical (synaptic) and electrical couplings is studied. Single neuron is modeled by van der Pol oscillator. Aim of work is to study of influence of coupling strength and frequency detuning between elements in the case of regime of sequential activity that is observed in ensemble of neuronlike elements with chemical inhibitory couplings. Method. The research is made with usage of analytical methods of nonlinear dynamics and computer modeling. Results. It was shown that adding of arbitrarily small electrical coupling to ensemble of van der Pol oscillators with chemical synaptic inhibitory couplings leads to the destruction of a stable heteroclinic contour between saddle limit cycles. It was also shown that nonidentity of elements (while electrical couplings are absent) do not lead to destruction of heteroclinic contour. This situation, in general, is not typical for such systems. Discussion. We suggest to consider the ensemble of elements as phenomenological model of neuronal network. Such approach has the following advantage: 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 also in real experiments. }}