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The practical damage of silicon bipolar devices subjected to mixed ionization and displacement irradiations is usually evaluated by the sum of separated ionization and displacement damages. However, recent experiments show clear difference between the practical and summed damages, indicating significant irradiation synergistic effects (ISEs). Understanding the behaviors and mechanisms of ISEs is essential to predict the practical damages. In this work, we first make a brief review on the state of the art, critically emphasizing on the difficulty encountered in previous models to understand the dose rate dependence of the ISEs. We then introduce in detail our models explaining this basic phenomenon, which can be described as follows. Firstly, we show our experimental works on PNP and NPN transistors. A variable neutron fluence and $γ$-ray dose setup is adopted. Fluence-dependent `tick'-like and sublinear dose profiles are observed for PNP and NPN transistors, respectively. Secondly, we describe our theoretical investigations on the positive ISE in NPN transistors. We propose an atomistic model of transformation and annihilation of $\rm V_2$ displacement defects in p-type silicon under ionization irradiation, which is totally different from the traditional picture of Coulomb interaction of oxide trapped charges in silica on charge carriers in irradiated silicon. The predicted novel dose and fluence dependences are fully verified by the experimental data. Thirdly, the mechanism of the observed negative ISE in PNP transistors is investigated in a similar way as in the NPN transistor case. The difference is that in n-type silicon, VO displacement defects also undergo an ionization-induced transformation and annihilation process. Our results show that, the evolution of displacement defects due to carrier-enhanced defect diffusion and reaction is the dominating mechanism of the ISEs.