Pump-controlled bifurcation cascade in a dissipative soliton fiber laser: From fixed points to attractor competition

The probabilistic selection of coexisting states is a widely observed phenomenon in nonlinear systems such as fluid or biological systems. While mode-locked lasers are typical nonlinear systems whose complex pulse dynamics have been extensively studied, the global bifurcation path leading to such probabilistic selection remains scarcely documented. Here, utilizing a mode-locked fiber laser as a rapid testbed, we report a pump-controlled bifurcation cascade evolving from a deterministic fixed-point to a probabilistic regime of attractor competition. This process begins with a stable dissipative soliton, transitions to a pulsating state via a Hopf bifurcation, and subsequently enters a multistable regime where the system probabilistically settles into either a stable or a periodic attractor. Numerical modeling reproduces this cascade, verifying that the observed competition is an intrinsic emergent behavior of the nonlinear dynamics. Crucially, our analysis reveals that the probabilistic state selection is governed by the relative geometric volumes of competing basins of attraction, rather than extrinsic noise. This work experimentally validates the concept of basin stability, offering critical insights for analyzing transient dynamics and ensuring reliable operation in high-dimensional dissipative systems.