  We use simulations to examine hysteresis and noise in a model system that
produces heterogeneous orderings including stripe and clump phases. In the
presence of a disordered substrate, these heterogeneous phases exhibit
1/f$^\alpha$ noise and hysteresis in transport. The noise fluctuations are
maximal in the heterogeneous phases, while in the uniform phases the hysteresis
vanishes and both $\alpha$ and the noise power decrease. We compare our results
to recent experiments exhibiting noise and hysteresis in high-temperature
superconductors where charge heterogeneities may occur.
