The spatial and temporal behavior of neutron distributions governed by the nonlinear diffusion equation approximation to neutron transport theory are considered in this paper. Stability criteria for the equilibrium states of various reactor feedback models are determined by the method of comparison functions. The comparison functions are used to construct simple solutions with error bounds to the equations considered. The two reactor models considered are the prompt feedback and the adiabatic model. The stability of the equilibrium state was found to be governed by the generalized buckling κ and its relationship to μ the lowest eigenvalue of the associated linear Helmholtz equation. Negative feedback is considered in both cases. Since the comparison functions bound the true solution from above and below, one can determine absolute errors of the approximations involved when constructing solutions. In a similar fashion, a bound on the maximum value of the excursion can also be obtained with little extra effort.