  We numerically solve the effective loop quantum cosmology dynamics for the
vacuum Bianchi type II and type IX spacetimes, in particular studying how the
Kasner exponents evolve across the loop quantum cosmology bounce. We find that
when the spatial curvature is negligible at the bounce then the Kasner
exponents transform according to the same simple equation as for a Bianchi type
I spacetime in effective loop quantum cosmology, while there are departures
from this transformation rule in cases where the spatial curvature is
significant during the bounce. We also use high-precision numerics to compute
the evolution of a Bianchi type IX spacetime through multiple bounces and
recollapses, and find indications of chaotic behaviour. Interestingly, the
numerics indicate that it is during the classical recollapse, and not the loop
quantum cosmology bounce, that nearby solutions diverge most strongly.
