Analysis of nonlinear reactor systems by forward and backward integration methods

In this paper, third-order nonlinear nuclear reactor systems are analyzed by plotting trajectories. The unique approach is that an accurate boundary of the asymptotic stability region can be found by first linearizing a system at an unstable singular point, such as a saddle point, and then plotting the trajectories starting from a choosing set of initial points very near the unstable singular point and on the surface spanned by the stable right eigenvector of the linearized system. In addition, the system characteristics, such as speed of response and damping, can be studied by plotting trajectories starting from a preselected sets of initial conditions. Both the forward and backward integration methods are used to calculate the trajectories with a computer. Two reactor systems are analyzed, and comparisons with the other methods in current literature are made.