4.3.1 Rhythmic inputs

Periodic pulse inputs were given by the expression

where ti*=2πωi for i = 1,2,… is the set of times at which pulses occur, ω is the frequency, w = 1000d/ω is the pulse width given the duty cycle d ∈ (0,1), * is the convolution operator, and s determines how square the pulse is, with s = 1 being roughly normal and higher s being more square. For our simulations, we took d = 1/4 and s = 25, and ω ranged over the set {0.25, 0.5, 1, 1.5, …, 22.5, 23}. Input pulses were normalized so that the total (integrated) input was 1 pA/s, and were then multiplied by a conductance varying from 0 to 4 in steps of 0.1.

For I_PP, the instantaneous phase ϕ_I(t) was obtained as the angle of the complex time series resulting from the convolution of I_PP with a complex Morlet wavelet having the same frequency as the input and a length of 7 cycles.