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 $r^{-\alpha }$, the functional dependence of the critical coupling exponent on the coupling constant ${\alpha }_c\mathrm{}\left(K\right)\mathrm{}$ 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.