This study reports the existence of tricorn-like structures of stable periodic orbits in the parameter plane of an optically injected semiconductor laser model (a continuous-time dynamical system). These tricorns appear inside tongue-like structures that are created through simple Shi’lnikov bifurcations. As the linewidth enhancement factor-α of the laser increases, these tongues invade the laser locking zone and extends over the zone of stable period-1 orbits. This invasion provokes a rich overlap dynamics of the parameter planes that produces an abundant multistability. As α increases, the tricorn exhibits a phenomenon of codimension-3 rotating in the clockwise and counterclockwise directions in the plane of the injected field rate K vs its detuning ω. We hope that the numerical evidence of the tricorns presented herein motivates the study of mathematical conditions for their genesis. We also encourage the experimental verification of these tricorn-like structures because our results also open new possibilities for optical switching between several different laser outputs in the neighborhood of these structures.

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