PRC

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.

Let a neuron be spiking and

T1=normal time periodT2=perturbed time period

The perturbation is happening at time ts, therefore,

ts/T1=phase before perturbationT2−ts=time to next spike

Then, the phase has become (T1−(T2−ts))/T1

This therefore gives the following phase difference,

Δϕ=new phase−old phase=((T1−(T2−ts))/T1)−ts/T1=(T1−T2)/T1

Here, T1, T2 are the timings. ts is the time of perturbation. T1 is the free running period and T2 is the perturbed period.

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