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The mechanisms of the multiplicity and bifurcation of detonation waves in 3D rotating detonation engines (RDEs) with cavity combustor and array-holes injection are numerically investigated. Array-holes injection is adopted to mimic the discontinuous distribution of reactants in real RDE experiments. Four kinds of injection patterns with different inlet-area ratios and four RDE models C1 - C4 of different cavity depths are employed. The result shows that as the inlet-area ratio increases the detonation waves number decreases generally. A more underlying mechanism of the multiplicity is assumed that the multiplicity of detonation waves is closely related to the inhomogeneous distribution of the detonable reactants, and the decrease of homogeneity of the detonable reactants (HDR) level causes the increase of wave number. The relative frequency's variance of the detonable mixture, as a metric of the HDR level, is calculated and the results show that the wave count decreases as the variance of the relative frequency decreases, which testifies to the rationality of our hypothesis. Model C2 shows a mode-locked state and exhibits a likelihood that the detonation mode may be more stable in these RDEs of specific configuration. Additionally, the process of bifurcation in cavity RDEs is tortuous, which is because the frequent disordered collision and quenching in the cavity delay the stable detonation waves' formation. And the mechanism of the periodic bifurcation in annular RDEs is related to the periodic distribution of the detonable reactant, which is verified by comparing the HDR level at different instants. The mode stability and propulsive performance are also mentioned and the cavity RDEs show a promising prospect in some cases. [ABSTRACT FROM AUTHOR]