Neural spike renormalization. Part I — Universal number 1 |
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Authors: | Bo Deng |
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Institution: | Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, United States |
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Abstract: | For a class of circuit models for neurons, it has been shown that the transmembrane electrical potentials in spike bursts have an inverse correlation with the intra-cellular energy conversion: the fewer spikes per burst the more energetic each spike is. Here we demonstrate that as the per-spike energy goes down to zero, a universal constant to the bifurcation of spike-bursts emerges in a similar way as Feigenbaum's constant does to the period-doubling bifurcation to chaos generation, and the new universal constant is the first natural number 1. |
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Keywords: | Circuit models of neurons Poincaré return maps Feigenbaum constant Period-doubling bifurcation Isospiking bifurcation Renormalization universality |
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