We explore experimentally and theoretically the dynamics of a DFB quantum well laser subject to external opticalfeedback from a mirror. With increasing feedback, the system exhibits the following dynamical scenario: an extremelysmall limit cycle appears first and is followed by a quasi-periodic regime, and then by three subsequent limit cycles withdifferent repetition rates. This sequence of limit cycles can be associated with the change of phase of the reflected fieldwhich reveals translational symmetry and the fact of periodic solutions coexistence which we confirm numerically. Theresults can be useful for applications in reservoir computing with phase space of coexisting limit cycles acting as anonlinear reservoir as well as for other applications.
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