Synchronization transitions in a growing network of star-coupled nonidentical semiconductor lasers

Synchronized dynamics emerge spontaneously in many systems that interacts through a common medium. Systems like yeast cell colonies, pedestrians walking in a bridge, or chemical oscillators in a Belousov-Zhabotinsky medium can achieve a synchronized state for large enough number of oscillators. Two types of these size controlled transitions have been reported in the literature depending, among other aspects, on the stiffness of the transition: Dynamical Quorum Sensing (DQS) that is an abrupt transition and Crowd Synchrony (CS) that is a progressive transition. There are many examples showing that semiconductor lasers are a good testing bench for different nonlinear dynamics and we show that also in this case they can help to better understand DQS and CS. We show that nonidentical semiconductor lasers with delayed coupling allow the existence of both synchronization transitions where the type of transition is controlled by the pump current of the lasers. Furthermore, we discover a double transition to synchronization in large enough systems that occurs back-to-back when a control parameter is increased. We characterize the double transition introducing two different, but individually self consistent, large M scalings of the governing equations. We also derive the analytical expression that define the critical parameters where the first and second transition occurs.