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Home » Issues » Archive of Issues » 2016 - 4 issue » pp. 453-462

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Russia Yekaterinburg
Year
2016
Volume
26
Issue
4
Pages
453-462
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Section Mathematics
Title Noise-induced intermittency and transition to chaos in the neuron Rulkov model
Author(-s) Bashkirtseva I.A.a, Nasyrova V.M.a, Ryashko L.B.a, Tsvetkov I.N.a
Affiliations Ural Federal Universitya
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
DOI 10.20537/vm160401
Received 27 September 2016
Language Russian
Citation Bashkirtseva I.A., Nasyrova V.M., Ryashko L.B., Tsvetkov I.N. Noise-induced intermittency and transition to chaos in the neuron Rulkov model, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 4, pp. 453-462.
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