Dynamical systems analysis of spike-adding mechanisms in transient bursts

DOI10.1186/2190-8567-2-7zbMath1291.92043OpenAlexW2145391238WikidataQ41166165 ScholiaQ41166165MaRDI QIDQ2251504

Krasimira Tsaneva-Atanasova, Jakub Nowacki, Hinke M. Osinga

Publication date: 14 July 2014

Published in: The Journal of Mathematical Neuroscience (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/2190-8567-2-7

zbMATH Keywords

dynamical systemsgeometric singular perturbation theorytransient behaviourburstspike adding

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Neural biology (92C20) Dynamical systems in biology (37N25) Multiple scale methods for ordinary differential equations (34E13)

Related Items (18)

Spike-adding in parabolic bursters: the role of folded-saddle canards ⋮ Canard solutions in neural mass models: consequences on critical regimes ⋮ Bifurcation and Spike Adding Transition in Chay–Keizer Model ⋮ Continuation-Based Numerical Detection of After-Depolarization and Spike-Adding Thresholds ⋮ Canard-induced complex oscillations in an excitatory network ⋮ Symmetric bursting behaviors in the generalized FitzHugh-Nagumo model ⋮ Emergence of Canard induced mixed mode oscillations in a slow-fast dynamics of a biophysical excitable model ⋮ Methods to assess binocular rivalry with periodic stimuli ⋮ Unpeeling a Homoclinic Banana in the FitzHugh--Nagumo System ⋮ Spike-adding structure in fold/hom bursters ⋮ On analysis of inputs triggering large nonlinear neural responses slow-fast dynamics in the wendling neural mass model ⋮ A Surface of Heteroclinic Connections Between Two Saddle Slow Manifolds in the Olsen Model ⋮ Homoclinic organization in the Hindmarsh–Rose model: A three parameter study ⋮ Spike-adding canard explosion in a class of square-wave bursters ⋮ Mixed-mode bursting oscillations: Dynamics created by a slow passage through spike-adding canard explosion in a square-wave burster ⋮ Spike-Adding in a Canonical Three-Time-Scale Model: Superslow Explosion and Folded-Saddle Canards ⋮ Saddle slow manifolds and canard orbits in \(\mathbb{R}^{4}\) and application to the full Hodgkin-Huxley model ⋮ Symmetric Fold/Super-Hopf Bursting, Chaos and Mixed-Mode Oscillations in Pernarowski Model of Pancreatic Beta-Cells

Uses Software

• HomCont

Cites Work

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• Computing Slow Manifolds of Saddle Type
• NEURAL EXCITABILITY, SPIKING AND BURSTING
• Canards in \(\mathbb{R}^3\)

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