Geodesic
Excitation of a Group of Two Hindmarsh – Rose
Russian journal of nonlinear dynamics, Tome 19 (2023) no. 1, pp. 19-34

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We study a model of three Hindmarsh – Rose neurons with directional electrical connections. We consider two fully-connected neurons that form a slave group which receives the signal from the master neuron via a directional coupling. We control the excitability of the neurons by setting the constant external currents. We study the possibility of excitation of the slave system in the stable resting state by the signal coming from the master neuron, to make it fire spikes/bursts tonically. We vary the coupling strength between the master and the slave systems as another control parameter. We calculate the borderlines of excitation by different types of signal in the control parameter space. We establish which of the resulting dynamical regimes are chaotic. We also demonstrate the possibility of excitation by a single burst or a spike in areas of control parameters, where the slave system is bistable. We calculate the borderlines of excitation by a single period of the excitatory signal.
Keywords: neuronal excitability, Hindmarsh – Rose model.
Mots-clés : chaos 
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     author = {I. R. Garashchuk and D. I. Sinelshchikov},
     title = {Excitation of a {Group} of {Two} {Hindmarsh} {\textendash} {Rose}},
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     pages = {19--34},
     publisher = {mathdoc},
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     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2023_19_1_a1/}
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I. R. Garashchuk; D. I. Sinelshchikov. Excitation of a Group of Two Hindmarsh – Rose. Russian journal of nonlinear dynamics, Tome 19 (2023) no. 1, pp. 19-34. http://geodesic.mathdoc.fr/item/ND_2023_19_1_a1/