The Monte Carlo code TRIPOLI-5 is under development with the mid-term aim of simulating nuclear reactor behavior under both steady-state and transient conditions. This is achieved by leveraging high-performance computing (HPC) architectures and natively integrating physical feedback effects. Methods for addressing non-stationary transport problems are categorized into three main approaches: the point kinetic approximation, the determination of the asymptotic behaviour, and solving the exact kinetic equations which allows for a comprehensive characterization of core behavior. In this PhD thesis, we propose to evaluate the performance of these three approaches within the HPC context of TRIPOLI-5 and subsequently implement them by leveraging and generalizing the strategies derived from previous work. In particular, an additional challenge in this thesis will involve addressing photonuclear reactions, which induce a coupling between neutron and photon tranport equations. The developments achieved during this thesis will then be applied to the ZOE pile, France's first nuclear reactor, built by the CEA at the Fontenay-aux-Roses site, which achieved criticality on December 15, 1948. A set of experimental measurements available in historical reports will provide a validation basis for the reactor kinetics analysis methods developed in TRIPOLI-5. Since the ZOE pile was heavy-water moderated, photonuclear reactions on deuterium must be explicitly accounted for to accurately determine the evolution of reactor kinetics.