Canards existence in Fitzhugh-Nagumo and Hodgkin-Huxley neuronal models

DOI10.1155/2015/342010zbMath1394.34115arXiv1808.08109OpenAlexW3105912739WikidataQ59118068 ScholiaQ59118068MaRDI QIDQ1665395

Jean-Marc Ginoux, Jaume Llibre

Publication date: 27 August 2018

Published in: Mathematical Problems in Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.08109

Mathematics Subject Classification ID

Neural biology (92C20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Canard solutions to ordinary differential equations (34E17)

Related Items (5)

Canards Existence in the Hindmarsh–Rose Model ⋮ Mixed mode oscillations and phase locking in coupled FitzHugh-Nagumo model neurons ⋮ Synchronization and Pattern Formation in a Memristive Diffusive Neuron Model ⋮ Canards Existence in the Hindmarsh–Rose model ⋮ A partially averaged system to model neuron responses to interferential current stimulation

Cites Work

• The singularly perturbed Hodgkin-Huxley equations as a tool for the analysis of repetitive nerve activity
• Geometric singular perturbation theory for ordinary differential equations
• Giant squid-hidden canard: the 3D geometry of the Hodgkin-Huxley model
• Canards existence in Memristor's circuits
• Perturbation singulière en dimension trois : canards en un point pseudo-singulier nœud
• HODGKIN–HUXLEY AXON IS MADE OF MEMRISTORS
• À propos de canards (Apropos canards)
• Existence and Bifurcation of Canards in $\mathbbR^3$ in the Case of a Folded Node
• THE ASYMPTOTIC STRUCTURE OF THE HODGKIN–HUXLEY EQUATIONS
• Canards in \(\mathbb{R}^3\)
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