20
Figure 2.4 shows the location in the complex plane of the eigenvalues of the matrix
A given in (2.13). There is one complex pair: λ ≈ —0.19 ± 0.38г. From the imaginary
part we obtain ωr ≈ 61.5 Hz. This is close to the actual resonant frequency ωτ = 67
Hz, which can be computed numerically via a parameter sweep or by using a ZAP
current
ʃzʌp(t) = αsin(6tc), (2.16)
which is a just a sine current with a time-dependent frequency. The frequency re-
sponse to (2.16) is then computed as the Fourier transform of the voltage divided by
the Fourier transform of the input current (Puil et al., 1986).
2.3 Active and Quasi-Active Branched Neurons
The notions of active and quasi-active will now be extended to branched neurons
with accurate morphologies, general Hodgkin-Huxley-Style kinetics, and spatially-
distributed synaptic inputs. These three features of realistic neuronal models make
the modeling process more complex by requiring that the following be taken into
account:
• Continuity of potential and current balance must be enforced at junction points.
• The “sealed end” condition must be enforced at the distal end of branches with
no children.
Branch radii and ionic conductances can be spatially-varying.
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