This paper aims to investigate the stability of a coupled model including the inherently linear and stochastic Dynamic Monte Carlo (DMC) method and a nonlinear but deterministic thermal-hydraulics solver, whose instabilities may happen and lead to biased solutions. Due to the immense computational effort needed for even a single transient calculation by DMC, stability analysis is proposed to be performed on a low-dimensional model that adequately describes key issues of the full-scale calculation. This low-dimensional model is constructed by coupling the Stochastic Point-Kinetics equation (SPKe) with non-analog Monte Carlo noise to a time-dependent thermal-hydraulics model, resulting in a stochastic dynamical system. We presented the stability of the low-dimensional model by analyzing its fixed points and attractors during negative and positive feedback. The results showed that a sensitive region of initial conditions can exist in the presence of multiple attractors, where the noise decides the ending state of each path.