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In previous studies, a simplified stochastic model (called the stochastic space-dependent kinetics model, SSKM) based on the forward stochastic model in the stochastic kinetics theory and the Itô stochastic differential equations was developed for the analysis of monoenergetic space-time nuclear reactor kinetics in one dimension. However, the behavior of the dynamic variations under a transient condition that plays a crucial role in operational and safety controls of nuclear power reactors has not been explicitly analyzed using this model. In this work, a numerical investigation is made using the SSKM in order to observe the random oscillations in population dynamics following various transients in subcritical and supercritical reactors. The results, which appear plausible on a physical basis, demonstrate that the behavior of the stochastic neutron and precursor distributions within a reactor can be induced using the SSKM.