Figure 1.
Numerical evaluation of the function as defined in (13) above.
Figure 2.
Simulation and differentiation of trajectories with different noise strengths.
Pairs of trajectories simulated using (4) with (A) onset rapidity and noise
and (B)
and
. (C,D) As described in the text, an exponential curve was fit to each of the trajectories simulated. (E,F) The calculated derivative of the trajectories in A) and B) plotted as function of the voltage.
Figure 3.
Comparison of simulations and theory for different parameter values.
Trajectories (10000) were simulated as in Figure 2 with the following sets of parameter values: (A) ,
and
, (B)
,
and
. On each plot the endpoints were grouped into bins of width
. The average voltage in each bin is plotted in magenta, this should be compared with the most likely onset voltage at each time point according to our analysis, plotted in red. Similarly the standard deviation in each bin is plotted in cyan, and can be compared with the standard deviation predicted by our analysis at each time point, plotted in green.
Figure 4.
The relationship between onset span and onset rapidity as derived in the text.
Here the solid blue dots are the simulation data points reported in [2], while the solid red, yellow and green dots are the experimental data points from [2] for cat visual cortex neurons classified electrophysiologically as regular spiking, fast rhythmic bursting, and fast spiking respectively. Data from many cells of each type is displayed in this plot. The curves show our analytical results for various values of the parameter .