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