On the asymptotic stability of nuclear reactors with arbitrary feedback

A sufficient condition for the asymptotic stability of nuclear reactors in terms of the equilibrium power level and delayed neutron parameters is presented. The integrodifferential point kinetics equation for an autonomous reactor with an arbitrary nonlinear feedback is written in the quasilinear form Q + w2Q = ef(Q,Q). The averaging principle is applied to investigate the stability of the amplitude of the fundamental harmonic of the true nonlinear series solution of this equation. Using a related theorem, a stability criterion is obtained, which is found to be somewhat more general tha some previously proposed criteria