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Description:
We consider two semiconductor lasers coupled face to face under the assumption that the delay time of the injection is small. The model under consideration consists of two coupled rate equations, which approximate the coupled Lang-Kobayashi system as the delay becomes small. We perform a detailed study of the synchronized and antisynchronized solutions for the case of identical systems and compare results from two models: with the delay and with instantaneous coupling. The bifurcation analysis of systems with detuning reveals that self-pulsations appear via bifurcations of stationary (i.e. continuous wave) solutions. We discover the connection between stationary solutions in systems with detuning and synchronous (also antisynchronous) solutions of coupled identical systems. We also identify a codimension two bifurcation point as an organizing center for the emergence of chaotic behavior.