Geodesic
Noise-induced intermittency and transition to chaos in the neuron Rulkov model
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 26 (2016) no. 4, pp. 453-462

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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, stochastic sensitivity function, noise-induced transitions, stochastic bifurcations.
Mots-clés : random perturbations, tangent bifurcation 
@article{VUU_2016_26_4_a0,
     author = {I. A. Bashkirtseva and V. M. Nasyrova and L. B. Ryashko and I. N. Tsvetkov},
     title = {Noise-induced intermittency and transition to chaos in the neuron {Rulkov} model},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {453--462},
     publisher = {mathdoc},
     volume = {26},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2016_26_4_a0/}
}
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I. A. Bashkirtseva; V. M. Nasyrova; L. B. Ryashko; I. N. Tsvetkov. Noise-induced intermittency and transition to chaos in the neuron Rulkov model. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 26 (2016) no. 4, pp. 453-462. http://geodesic.mathdoc.fr/item/VUU_2016_26_4_a0/