  We prove that that second-order (double-loop) chaotic sigma-delta schemes are
stable - within a certain parameter range, all state variables of the system
are guaranteed to remain uniformly bounded. To our knowledge this is the first
general stability result for chaotic sigma-delta schemes of order greater than
one. Invariably as the amount of expansion added to the system is increased,
the dynamic range of the input must get smaller for stability to be guaranteed.
We give explicit bounds on this trade-off and verify through numerical
simulation that these bounds are near-optimal.
