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 ωk, k = 1, . . . ,N. We introduce a learning rule which influences the ωk by driving the system towards a consensual oscillatory state in which all oscillators share a common frequency ωc. We are able to analytically calculate ωc. The network topology strongly affects the relaxation rate but not the ultimate consensual ωc. We report numerical simulations to show the learning mechanisms at work and confirm our theoretical assertions.