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

Evdokia Slepukhina, Irina Bashkirtseva and Lev Ryashko

Chaos, Solitons & Fractals, 2020, vol. 138, issue C

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.

Keywords: Birhythmicity; Spiking; Bursting; Neuron dynamics; Random disturbances; Stochastic sensitivity; Order-chaos transitions; Mahalanobis metrics (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S096007792030357X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:138:y:2020:i:c:s096007792030357x

DOI: 10.1016/j.chaos.2020.109958

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().