However, quadratic IF models do not satisfy the concavity assumption.
We classified the newborn EEG seizure components based on their parametric IF models using the following process.
Nonlinear IF models are able to produce different patterns of activity and excitability types while linear models do not.
As a consequence, the value of V k when the neuron can fire again is not a constant, as it is in classical IF models.
For a more thorough discussion of IF models and the challenges of analysing non-smooth dynamical systems we refer the reader to [58].
In IF models, the spike is thought as a punctual "event" (typically, an "instantaneous" pulse) while the synaptic response is described by a convolution kernel (the α-profile).
The iPRC for planar piece-wise linear IF models can also be computed explicitly [58], although we do not discuss this further here.
So taking the limit δ → 0 as well as τ refr → 0 induces pathologies not inherent to our approach but to IF models.
The IF models, f (t, Ψ), along with the set of parameters, Ψ, for these classes are given in Table1[16, 21, 31].
Although in the deterministic (noiseless) case, this is a simplifying feature allowing for example to fully characterize the asymptotic dynamics of (discrete time) IF models [32, 54], here, it somewhat renders more complex the analysis.
Just as for the IF models, the period of oscillation and decay rate depend on the final firing rate and input variance after the jump in input.
