Networks of mixed canonical-dissipative systems and dynamic hebbian learning

We study the dynamics of a network consisting of N diffusively coupled, stable- limit-cycle oscillators on which individual frequencies are parametrized by $w_k, k = 1, . . . ,N$. We introduce a learning rule which influences the wk by driving the system towards a consensual oscillatory state in which all oscillators share a common frequency $w_c$. We are able to analytically calculate $w_c$. The network topology strongly affects the relaxation rate but not the ultimate consensual $w_c$. We report numerical simulations to show the learning mechanisms at work and confirm our theoretical assertions.