We theoretically investigate the nonlinear dynamics and synchronization properties of two self-oscillating semiconductor lasers subject to optoelectronic mutual-coupling and feedback loops. The model is based on modified single-mode rate equations for the intracavity photon and carrier densities. The optoelectronic interactions take into account the finite propagation time of the optical and electrical signals. We provide a detailed stability and bifurcation analysis of the fixed points upon variation of the coupling and feedback strengths as well as the associated delay times. This allows us to predict a new scenario for the ``death by delay'' phenomenon where the delay time in the interaction between the physical units is not essential. We consider both oscillatory and chaotic behavior of the solitary lasers by changing the feedback conditions. We find different types of synchronization including identical, anti-phase and localized synchronization even for perfectly symmetric systems. When the lasers operate as two chaotic oscillators, we find that the isochronal (zero-lagged) state is stable within a large region in the parameter space. The width of the frequency lockbands (Arnold tongues) of two slightly mismatched lasers shows an interesting dependence with the coupling delay time.
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