This article is cited in 3 papers

MATHEMATICS

Noise-induced intermittency and transition to chaos in the neuron Rulkov model

I. A. Bashkirtseva^a, V. M. Nasyrova^a, L. B. Ryashko^a, I. N. Tsvetkov<sup>b

a</sup> Institute of Mathematics and Computer Science, Ural Federal University, pr. Lenina, 51, Yekaterinburg, 620000, Russia
^b Ural Federal University, pr. Lenina, 51, Yekaterinburg, 620000, Russia

Abstract: A discrete neuron model proposed by Rulkov is studied. In the deterministic version, this system simulates different modes of neural activity, such as quiescence, tonic and chaotic spiking. In the presence of random disturbances, another important mode of bursting characterized by the alternation of quiescence and excitement regimes can be observed. We study the probabilistic mechanisms of noise-induced transitions from quiescence to bursting in the zone of the tangent bifurcation. It is shown that such transitions are accompanied by a transformation of the system dynamics from regular to chaotic. For the analysis of these bifurcation phenomena, the stochastic sensitivity functions technique and method of confidence intervals are used.

Keywords: Rulkov model of neural activity, random perturbations, stochastic sensitivity function, tangent bifurcation, noise-induced transitions, stochastic bifurcations.

UDC: 51-76, 519.216

MSC: 39A50

Received: 27.09.2016

DOI: 10.20537/vm160401

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