I am trying to implement the Explosive synchronization in Kuramoto model.

I know that in the we have this equation[1]:

d theta/ dt = omega_i + K/N*abs(omega_i) * sum Cij * (sin(theta_j - theta_i)

where Cij is the connection matrix of BA network.

I increase the coupling progressively(with step 0.02) and compute the stationary value of the order parameter r.

How program should know that I am calculating the forward or backward curve?

I use the final phase state of the oscillators as initial phase of the oscillators at a larger(smaller) coupling. I use a normal distribution with scale 1 and mean of 0 for initial frequency of oscillators and I don't change it by increasing(decreasing) the coupling.

Am I in a correct path?

[1] Gómez-Gardeñes, J., Gómez, S., Arenas, A., & Moreno, Y. Explosive Synchronization Transitions in Scale-free Networks. PRL, 2011

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