  Mode-locked fiber lasers are one of the most important sources of ultra-short
pulses. However, A unified description for the rich variety of states and the
driving forces behind the complex and diverse nonlinear behavior of mode-locked
fiber lasers have yet to be developed. Here we present a comprehensive
theoretical framework based upon complexity science, thereby offering a
fundamentally new way of thinking about the behavior of mode-locked fiber
lasers. This hierarchically structured frame work provide a model with and
changeable variable dimensionality resulting in a simple and elegant view, with
which numerous complex states can be described systematically. The existence of
a set of new mode-locked fiber laser states is proposed for the first time.
Moreover, research into the attractors' basins reveals the origin of
stochasticity, hysteresis and multistability in these systems. These findings
pave the way for dynamics analysis and new system designs of mode-locked fiber
lasers. The paradigm will have a wide range of potential applications in
diverse research fields.
