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Stochastic spiking-bursting transitions in a neural birhythmic 3D model with the Lukyanov-Shilnikov bifurcation

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  • Slepukhina, Evdokia
  • Bashkirtseva, Irina
  • Ryashko, Lev

Abstract

A three-dimensional neuron model with the Lukyanov–Shilnikov bifurcation is considered in the birhythmicity zone where two limit cycles representing tonic spiking and bursting coexist. We show that in this parameter zone noise induces diverse stochastic phenomena: (i) transitions between coexisting oscillatory attractors; (ii) coherence resonances; (iii) order-chaos transformations. In our study of these phenomena, we take into account a mutual arrangement of coexisting spatial oscillatory attractors and separate surface. The parametric analysis of probabilistic mechanisms of stochastic phenomena found by numerical simulations is carried out on the base of the theoretical approach combining stochastic sensitivity functions, confidence domains and Mahalanobis metrics.

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  • Slepukhina, Evdokia & Bashkirtseva, Irina & Ryashko, Lev, 2020. "Stochastic spiking-bursting transitions in a neural birhythmic 3D model with the Lukyanov-Shilnikov bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    • Handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s096007792030357x
    DOI: 10.1016/j.chaos.2020.109958
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