Abstract
By injecting an electrical current control stimulus into a neuron, one can change its inter-spike intervals. In this paper, we investigate the time optimal control problem for periodically firing neurons, represented by different one-dimensional phase models, and find analytical expressions for the minimum and maximum values of inter-spike intervals achievable with small bounded control stimuli. We consider two cases: with a charge-balance constraint on the input, and without it. The analytical calculations are supported with numerical results for examples of qualitatively different neuron models.
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This work was supported by the National Science Foundation Grant NSF-0547606 and 1000678.
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Nabi, A., Moehlis, J. Time optimal control of spiking neurons. J. Math. Biol. 64, 981–1004 (2012). https://doi.org/10.1007/s00285-011-0441-5
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DOI: https://doi.org/10.1007/s00285-011-0441-5