  The erraticity in the random-cascading $\alpha$ model is revisited. It is
found that in contrary to the previous expectation, even in the pure
single-$\alpha$ random-cascading model without putting in any particle there
exists erraticity behavior and the corresponding entropy indices do not vanish.
This means that the dynamical fluctuations in a pure single-$\alpha$ model
already fluctuate event-by-event. Models with multiple-$\alpha$ strengthen this
fluctuation. Taking double-$\alpha$ model as example, the variation of the
event-space fluctuation strength with the mixing ratio of the two $\alpha$'s is
studied in some detail. The influence of particle number on the results when
particles are putted into the system is also investigated.
