We investigate the dynamics of a system that consists of ultra-cold three-level atoms interacting with radiation fields. We derive the analytical expressions for the population dynamics of the system, particularly, in the presence and absence of nonlinear collisions by considering the rotating wave approximation (RWA). We also reanalyze the dynamics of the system beyond RWA and obtain the state vector of the system to study and compare the time behavior of population inversion. Our results show that the system undergoes two pure quantum phenomena, i.e., the collapse–revival and macroscopic quantum self-trapping due to nonlinear collisional interactions. The occurrence of such phenomena strongly depends on the number of atoms in the system and also the ratio of interaction strengths in the considered system. Finally, we show that the result of the perturbed time evolution operator up to the second-order is in agreement with the numerical solution of the Schrödinger equation. The results presented in the paper may be useful for the design of devices that produce a coherent beam of bosonic atoms known as an atom laser.