Interspike interval correlations in neuron models with adaptation and correlated noise
Fig 2
Serial correlation coefficients for the adaptive QIF (Theta) model with colored noise.
Panel A shows the transformed membrane potential θ(t) = 2tan−1v(t), adaptation current a(t) and colored noise η(t) with spike times {ti}, ISIs {Ti} and peak adaptation values {ai}. Panel B displays the deterministic limit cycle (dashed line) and exemplary noisy trajectory (solid line) in the phase plane (θ, a). Note that the jump is of constant size Δ/τa, while the voltage or equivalently phase always resets to a fixed value θR. Panel C depicts the corresponding type I PRC quantifying the QIF model’s response characteristics. For a non-adaptive QIF model the PRC would be symmetric around T*/2; for the adaptive QIF, however, the maximum is shifted towards the right, i.e. the neuron is particularly sensitive to stimuli applied at the end of the ISI. Panel D shows the SCC with initial, slightly positive correlation coefficient due to positively correlated noise and subsequent negative correlations governed by adaptation. This pattern cannot be described by a single geometric sequence. Parameters: μ = 5, τa = 6, Δ = 18, τη = 4, σ2 = 0.5, D = 0 and resulting T* ≈ 4.0 and coefficient of variation CV ≈ 0.2.