A novel canard-based mechanism for mixed-mode oscillations in a neuronal model

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dc.creatorJalics, Jozsi
dc.creatorKrupa, Martin
dc.creatorRotstein, Horacio G.
dc.date2008-04-05
dc.date.accessioned2026-07-07T09:30:41Z
dc.date.available2026-07-07T09:30:41Z
dc.descriptionWe analyze a biophysical model of a neuron from the entorhinal cortex that includes persistent sodium and slow potassium as non-standard currents using reduction of dimension and dynamical systems techniques to determine the mechanisms for the generation of mixed-mode oscillations. We have found that the standard spiking currents (sodium and potassium) play a critical role in the analysis of the interspike interval. To study the mixed-mode oscillations, the six dimensional model has been reduced to a three dimensional model for the subthreshold regime. Additional transformations and a truncation have led to a simplified model system with three timescales that retains many properties of the original equations, and we employ this system to elucidate the underlying structure and explain a novel mechanism for the generation of mixed-mode oscillations based on the canard phenomenon. In particular, we prove the existence of a special solution, a singular primary canard, that serves as a transition between mixed-mode oscillations and spiking in the singular limit by employing appropriate rescalings, center manifold reductions, and energy arguments. Additionally, we conjecture that the singular canard solution is the limit of a family of canards and provide numerical evidence for the conjecture.
dc.description46 pages, 17 figures
dc.identifierhttps://arxiv.org/abs/0804.0829
dc.identifierhttp://arxiv.org/abs/0804.0829
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158197
dc.subjectDynamical Systems
dc.subjectBiological Physics
dc.subjectNeurons and Cognition
dc.subject37N25
dc.titleA novel canard-based mechanism for mixed-mode oscillations in a neuronal model
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