We analyze the dynamical instabilities of an additive-pulse-modelocked
Nd:YAG laser; period doubling up to period 8, quasi-periodicity and h
igh-dimensional chaos are observed. Experimental and numerical data ar
e analyzed using bifurcation diagrams, spectrograms, and Grassberger-P
rocaccia analysis. It is shown that the instability threshold is not a
ffected if the fiber resonator length is chosen as an integer multiple
of that of the main resonator, as is often done. However, the dynamic
s beyond the bifurcation depends on the length ratio in a systematic m
anner.