Determination of Stability Domains in Point Reactor Dynamics

Nonlinear stability criteria for reactors (Welton, Popov, etc.) can only be used when the reactor is linearly stable at all equilibrium power levels. This paper contains four methods of analysis of nonlinear stability that can be used when the reactors are unstable above a certain equilibrium power. The topological method and the second Liapunov method are often of no practical interest, while the Aizermann and Rosen methods are applicable irrespective of the complexity of the system. The different methods are compared in the case of a reactor with a prompt-positive temperature coefficient and a slow-negative temperature coefficient.