Phase transitions in nonlinear oscillator chains

It is shown numerically that a one-dimensional system of coupled disparate nonlinear oscillators undergoes a phase transition from a synchronized to a desynchronized state as the range of interactions is decreased. Using a coupling that decreases with distance as r^-α, the functional dependence of the critical coupling exponent on the coupling constant αc(K) is mapped out and the nature of the transition is discussed. Previously studied models and results are recovered in the appropriate limits of the coupling exponent.