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arXiv · 1807.10824

Mixed mode oscillations and phase locking in coupled FitzHugh-Nagumo model neurons

Elizabeth N. Davison·Zahra Aminzare·Biswadip Dey·Naomi Ehrich Leonard
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Abstract

We study the dynamics of a low-dimensional system of coupled model neurons as a step towards understanding the vastly complex network of neurons in the brain. We analyze the bifurcation structure of a system of two model neurons with unidirectional coupling as a function of two physiologically relevant parameters: the external current input only to the first neuron and the strength of the coupling from the first to the second neuron. Leveraging a timescale separation, we prove necessary conditions for multiple timescale phenomena observed in the coupled system, including canard solutions and mixed mode oscillations. For a larger network of model neurons, we present a sufficient condition for phase locking when external inputs are heterogeneous. Finally, we generalize our results to directed trees of model neurons with heterogeneous inputs.

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Elizabeth N. Davison, Zahra Aminzare, Biswadip Dey, Naomi Ehrich Leonard. 2018-07-27. Mixed mode oscillations and phase locking in coupled FitzHugh-Nagumo model neurons. https://doi.org/10.1063/1.5050178

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