Bistabilities between a steady (or pulsating, chaotic) and different pulsating regimes are investigated for an optically injected semi-conductor laser. Both numerical and experimental studies are reported for continuous-wave single-mode semiconductor distributed-feedback lasers emitting at 1.55 microm. Hysteresis are driven by either changing the optically injected power or the frequency difference between both lasers. The effect of the injected laser pumping rate is also examined. Systematic mappings of the possible laser outputs (injection locking, bimodal, wave mixing, chaos or relaxation oscillations) are carried out. At small pumping rates (1.2 times threshold), only locking and bimodal regimes are observed. The extent of the bistable area is either 11 dB or 35 GHz, depending on the varying parameters. At high pumping rates (4 times threshold), numerous injection regimes are observed. Injection locking and its bistabilities are also reported for secondary longitudinal modes.