{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:54:06Z","timestamp":1777647246545,"version":"3.51.4"},"reference-count":38,"publisher":"World Scientific Pub Co Pte Lt","issue":"12","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,11]]},"abstract":"<jats:p> The stochastically forced three-dimensional Hindmarsh\u2013Rose model of neural activity is considered. We study the effect of random disturbances in parametric zones where the deterministic model exhibits mono- and bistable dynamic regimes with period-adding bifurcations of oscillatory modes. It is shown that in both cases the phenomenon of noise-induced bursting is observed. In the monostable zone, where the only attractor of the system is a stable equilibrium, this effect is connected with a stochastic generation of large-amplitude oscillations due to the high excitability of the model. In a parametric zone of coexisting stable equilibria and limit cycles, bursts appear due to noise-induced transitions between the attractors. For a quantitative analysis of the noise-induced bursting and corresponding stochastic bifurcations, an approach based on the stochastic sensitivity function (SSF) technique is applied. Our estimations of the strength of noise that generates such qualitative changes in stochastic dynamics are in a good agreement with the direct numerical simulation. A relationship of the noise-induced generation of bursts with transitions from order to chaos is discussed. <\/jats:p>","DOI":"10.1142\/s0218127416300329","type":"journal-article","created":{"date-parts":[[2016,11,22]],"date-time":"2016-11-22T07:46:26Z","timestamp":1479800786000},"page":"1630032","source":"Crossref","is-referenced-by-count":29,"title":["Stochastic Bifurcations and Noise-Induced Chaos in 3D Neuron Model"],"prefix":"10.1142","volume":"26","author":[{"given":"Irina","family":"Bashkirtseva","sequence":"first","affiliation":[{"name":"Institute of Mathematics and Computer Science, Ural Federal University, Lenina, 51, Ekaterinburg 620083, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sergei","family":"Fedotov","sequence":"additional","affiliation":[{"name":"School of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lev","family":"Ryashko","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and Computer Science, Ural Federal University, Lenina, 51, Ekaterinburg 620083, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Evdokia","family":"Slepukhina","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and Computer Science, Ural Federal University, Lenina, 51, Ekaterinburg 620083, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,11,21]]},"reference":[{"key":"S0218127416300329BIB001","volume-title":"Nonlinear Dynamics of Chaotic and Stochastic Systems. 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