Impact of delayed neutrons on bifurcation and stochastic self-excited oscillations in nuclear reactors with discrete control systems

The present study investigates the influence of delayed neutrons on stability boundaries, chaos, and bifurcation phenomena in nuclear reactors with discrete control systems. It focuses on a point kinetics model of a reactor with a regulatory system that includes a single group of delayed neutrons and temperature feedback related to either the moderator or fuel temperature, as well as power feedback. Bifurcation diagrams are used to examine the transition to chaos, an area previously underexplored. Our research includes the development of an analytical model and detailed numerical analysis to identify stability regions and chaotic dynamics in reactor models incorporating delayed neutrons. Furthermore, we introduce innovative one-dimensional piecewise linear maps that exhibit diverse behaviors, including periodic motion, n-band chaotic attractors, exterior crisis phenomena, type I intermittency, and periods of regular motion interrupted by short quasiperiodic motion and chaotic bursts. Comparisons are drawn between models with and without delayed neutrons.