Frequency entrainment in long chains of oscillators with random natural frequencies in the weak coupling limit
We study oscillator chains of the form phi(k)=omega(k)+K[Gamma(phi(k-1)-phi(k))+Gamma(phi(k+1)-phi(k))], where phi(k)is an element of[0,2pi) is the phase of oscillator k. In the thermodynamic limit where the number of oscillators goes to infinity, for suitable choices of Gamma(x), we prove that there is a critical coupling strength K-c, above which a stable frequency-entrained state exists, but be