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This is because the membrane potential evolution integrates its past values and the past influence of the network via the leak term.
What we need is therefore to define the membrane potential evolution before the spike, given by (1), and after the spike, given by (4) (see Figure 1).
The LIF models have been extensively applied to model the membrane potential evolution in single neurons in computational neuroscience (for reviews, see [20, 21]).
(c) An example realization of membrane potential evolution, Eq. (1), responding to the sinusoidal signal (s_{1}), and (d) responding to the constant signal (s_{0}).
As explained in the previous section, MAUDS tackles these problems with an initial broad identification of the down states by overcrossing two moving averages, and a later refinement of the initiation and termination points by a discrete processing of the membrane potential evolution in the transition interval.
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We show that functional hyperemia spatially overlaps but overestimates the maximal extent of each wave of increase in membrane potential during ictal evolution and propagation.
Right: corresponding time evolution of the membrane potential.
Fig. 3 Time evolution of the membrane potential and the adaptation variable in the FitzHugh-Nagumo model.
The evolution of a membrane potential for a LIF suprathreshold neuron ( a > 1 ) is reported in Figure 1(a).
More precisely, the evolution of the membrane potential follows, see [3 8] C m d V d t = − g L ( V − V L ) + I ( t ), (1.1).
Given the neuron i in a population α, the stochastic time evolution of the membrane potential is denoted by ((V^{i}_{t})).
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