How to get the PRC from timings (Notes)

The following method describes how can one obtain the phase reset curve (PRC) as a function of timings of pulses. IT turns out using the PRC of a system we could basically say a lot about the interactions between neurons without actually simulating the whole differential equations taking the maps route. I thought I will write this as a note for the future stupid me wondering why I chose this route.

So this makes the phase difference to be the following.

are the timings. ts is the time of perturbation. is the free running period and is the perturbed period.