Mathematics, Department of


Date of this Version



Published in Journal of Differential Equations 250 (2011), pp. 2940-2957 doi: 10.1016/j.jde.2010.10.002


Copyright © 2010 Elsevier Inc. Used by permission.


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.