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We are attempting to run simulations of the C. Elegans neuronal network by building upon work of the OpenWorm team. We are looking into implementing a neuron model that produces plateau potentials rather than action potentials, as suggested by this paper. Thanks to @Comte for pointing me to this paper (see this link for another question related to our project).

Here is my question: What are known-to-work mathematical models of neurons that produce plateau potentials, rather than action potentials? Ideally, the model should be formulated as a system of differential equations (as is for example the Hodgkin-Huxley model), hence easy to implement in NEURON.

(A note on my personal background: I am a student of mathematics, and this is a project for university.)

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i once wrote a paper doing biophysical modeling of neurons that could create plateau potentials. While the paper itself is not exactly what you are looking for, there should be lots of good references in there:
http://www.jneurosci.org/content/33/2/424.short
Sanders H, Berends M, Major G, Goldman MS, Lisman JE. (2013) NMDA and GABAB (KIR) Conductances: The “Perfect Couple” for Bistability. J. Neurosci. 33, 424–429

also, check other articles that cited that paper: https://scholar.google.com/scholar?cites=2120401607202660739

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