  Self-sustained current oscillation observed in spin-blockaded double quantum
dots is explained as a consequence of periodic motion of dynamically polarized
nuclear spins (along a limit cycle) in the spin-blockaded regime under an
external magnetic field and a spin-transfer torque. It is shown, based on the
Landau-Lifshtz-Gilbert equation, that a sequence of semistable limit cycle,
Hopf and homoclinic bifurcations occurs as the external field is tuned. The
divergent period near the homoclinic bifurcation explains well why the period
in the experiment is so long and varies by many orders of magnitudes.
