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This paper presents a model describing self-mode locking (SML) and sustained self-pulsing (SSP) in a unidirectional ring-fiber laser using only the interaction between the saturated population inversion and the optical signal circulating in the laser cavity. Gain saturation alone is used to explain SML behavior close to laser threshold and the sharp transition to an SSP regime. The model also describes self-pulsing inhibition to the profit of SML for a sufficiently high pump power. Experimental results agree with most model predictions, but the overestimation of the self-pulsing threshold suggests that the phenomenon is furthered by an effect other than gain saturation.