  We experimentally study the nonlinear dynamics of a femtosecond ytterbium
doped mode-locked fiber laser. With the laser operating in the pulsed regime a
route to chaos is presented, starting from stable mode-locking, period two,
period four, chaos and period three regimes. Return maps and bifurcation
diagrams were extracted from time series for each regime. The analysis of the
time series with the laser operating in the quasi mode-locked regime presents
deterministic chaos described by an unidimensional Rossler map. A positive
Lyapunov exponent $\lambda = 0.14$ confirms the deterministic chaos of the
system. We suggest an explanation about the observed map by relating gain
saturation and intra-cavity loss.
