Erraticity in Random-Cascading α Model

The erraticity in the random-cascading α model is investigated. It is found that, contrary to the previous expectation, even in the pure single-α random-cascading model without putting in any particle, erraticity behaviour exists and the corresponding entropy indices do not vanish. This means that the dynamical fluctuations in a pure single-α model have already occured event-by-event. The models with multiple-αstrengthen this fluctuation. Taking double-α model as example, the variation of the event space fluctuation strength with the mixing ratio of the two αs is studied in some detail. The influence of particle number on the results when the particles are put into the system is also investigated.