Hysteresis phenomenon in nuclear reactor dynamics

This paper applies a nonlinear analysis method to show that hysteresis phenomenon, due to the Saddle-node bifurcation, may occur in the nuclear reactor. This phenomenon may have significant effects on nuclear reactor dynamics and can even be the beginning of a nuclear reactor accident. A system of four dimensional nonlinear ordinary differential equations was considered to study the hysteresis phenomenon in a typical nuclear reactor. It should be noted that the reactivity was considered as a nonlinear function of state variables. The condition for emerging hysteresis was investigated using Routh-Hurwitz criterion and Sotomayor's theorem for saddle node bifurcation. A numerical analysis is also provided to illustrate the analytical results.