We studied a Kuramoto type model for phase-locking with a Hebbian type dynamics governing the coupling stregths for the interoscillator potentials. We found that the fixed points and stability of this model could be reduced to questions about the fixed points and stability of a Kuramoto model with fixed (constant) edge weights. You can read about it on the ArXiv.

The code for Figures 1 and 2 and for Figures 3 and 4 are "hardwired" for the three oscillator Kuramoto model on the complete graph, but the code to produce graphs 5 through 8 will work on essentially any graph. It is currently set up for a random preferential attachment graph of Albert and Barabasi, but it is easy to change to any desired graph. The mstrix "Filter" contains the adjacency matrix for the graph. Changing this will produce the Hebbian Kuramoto dynamics for any desired graph. Mathematica has built in routines to generate many type of random networks: Strogatz/watts, Erdos Renyi, etc.