Synchronization of weakly stable oscillators and semiconductor laser arrays

We study the synchronization properties of an array of nonidentical globally coupled limit cycle oscillators. Above a critical coupling strength, some oscillators undergo a self-pulsing instability. We study analytically the synchronization conditions below and above this instability threshold, thus removing the usual restriction of limit cycle stability. Self-pulsing decreases the order parameter and synchronization degradation can be reduced by delaying the coupling among the oscillators. Semiconductor lasers coupled by an external mirror are used as a convenient realization of that model.