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Ultrafast fiber lasers offer a unique opportunity to implement optically a Poincaré mapping in the phase space of a variety of complex dissipative dynamical systems operating far from the equilibrium. Understanding of such complex optical dynamical systems revealing, for instance, ultrafast dynamics of the dissipative solitons (DSs) and more complex regimes is important for advancing specification and performance of the mode‐locked lasers used in a vast number of applications ranging from spectroscopy and medicine to metrology and telecom. Here, using the mode‐locked fiber laser as a test‐bed, the Shilnikov‐type ultrafast dynamics taking the form of randomly switching between noise‐like pulsing and quasi‐continuous‐wave regimes is experimentally demonstrated. The transient coherence recovery is revealed, during which the noise‐like pulse (NLP) is transformed into a coherent DS state and then returned to an incoherent NLP state. The demonstrated alternation of mode synchronization and desynchronization is both of practical importance for developing new types of partially mode‐locked lasers and of the fundamental interest for the nonlinear science in the context of revealing routes to the turbulence in distributed nonlinear systems. [ABSTRACT FROM AUTHOR]

• GHz pulse bursts with tunable intra-burst repetition rate and number of pulses are demonstrated experimentally and numerically based on the inherent nature of the fiber lasing cavity for the first time. • With the increase of pump power, only the number of pulses per burst increases one by one in the positive feedback region of the NPR SA, while only the number of pulses per burst increases one by one in the inverse feedback region. • The 22.8-GHz intra-burst repetition rate is the highest value in all-fiber laser systems. Optical pulse bursts are multiple pulses that arise from the balance between attractive and repulsive effects and are used for pulsed laser deposition, flow measurement, various micromachining, spectroscopic, and biomedicine. Different application fields have special requirements for the pulse burst, such as burst width, frequency, number of pulses per burst, and the pulse interval etc. Here, we propose and demonstrate the generation of GHz pulse bursts with both tunable pulse number and pulse interval in a nonlinear polarization rotation (NPR) mode-locked fiber laser for the first time. Taking advantage of the sinusoidal saturated absorption of the NPR, with the increase of pump power, only the number of pulses per burst increases one by one in a relatively low pump power range, while only the pulse interval increases gradually in a high pump power range. In addition, one pulse burst with a 22.8-GHz repetition rate is achieved, which is the highest intra-burst repetition rate directly obtained in all-fiber lasers to the best of our knowledge. The numerical results agree qualitatively well with the experiments. Our work gives an insight into the formation of pulse bursts in mode-locked fiber lasers. [ABSTRACT FROM AUTHOR]