  Period doubling is a universal bifurcation of central importance in all
disciplines of nonlinear science, which generally signals the existence of
chaotic dynamics in the vicinity of the system parameters. Although observed in
diverse ultrafast laser configurations, there is still no consensus on its
physical origin. The observations also include other types of pulsating
dissipative solitons, with either short or long periods. Real time spectral
characterization allows to investigate optical spectral oscillations, whose
features reveal the intracavity dynamics leading to instabilities. Following a
contextual review, this article presents a variety of period doubling dynamics
manifesting in the spectral domain of dissipative solitons. These dynamics are
obtained with ultrafast fiber lasers featuring either anomalous or normal
dispersion. It reveals a sequence of period doubling bifurcations and
instabilities within transient dynamics, unveiling intertwined bifurcations and
the entrainment of new pulsating frequencies. The oscillating frequencies tend
to lock to the integral of roundtrip numbers as well as coexist with period
doubling, demonstrating new combinations of the period doubling bifurcation
with other bifurcations. These experimental findings are confirmed by numerical
simulations, emphasizing both the universality of the period doubling
bifurcations and their potentially highly complicated manifestations within
ultrafast laser systems.
