Stability analysis in nuclear reactor using Lyapunov exponent

A simple model for nuclear reactor is proposed. With increasing the fuel concentration, our minimal model shows two successive phases; subcritical and supercritical. In subcritical regime, the neutron population grows with increasing the fuel concentration. In the supercritical state, the Lyapunov exponent is positive implying that the neutron diffusion phenomena are spatiotemporal chaos. In the present paper, the infinite multiplication factor curve is qualitatively reproduced for fuel concentration. We have derived the critical fuel concentration based on the Lyapunov exponents. The basic objective of the work is to improve the prediction of the critical neutron population with respect to the fuel concentration.