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In this work, we establish a unified temporal-spatial model to study the temporal-spectral dynamics of Ytterbium-doped fiber lasers (YDFLs). Different from the previously reported theories, this model is capable of obtaining the temporal property of YDFLs from the relaxation oscillation region to the relative stable region in the time window of millisecond scale with the time resolution of sub-nanosecond scale. The simulation results reveal that the three temporal instabilities, i.e. sustained self-pulsing (SSP), self-mode locking (SML) and turbulence-like pulsing (TLP), coexist in a multilongitudinal mode YDFL. When the output power evolution of the YDFL is observed in different time scales, different temporal instability phenomena dominate in the observation. Along with the increase of pump power, a single regular SML pulse would gradually break up into irregular TLP pulses and the life of the SSP pulse envelop would decrease. Besides, the spectral evolution property of the YDFLs at different pump powers are given and significant spectral broadening is observed.
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