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.