Local Bifurcation analysis of two dimensional nuclear reactor Dynamics with reactivity perturbation

In this paper, a two-dimensional dynamical model of a nuclear reactor is described. First the stability of original two-dimensional equations, involving neutron density and fuel temperature has been examined. The nuclear reactor is assumed as a closed dynamical system that its future is only based on its state variables. Then we entered perturbation terms in to the reactivity function. These perturbations can take place in normal operation or in accidents. Finally we obtain the conditions that the system experiences various bifurcations. In this study, we examined the local bifurcations such as saddle-node, transcritical and pitchfork bifurcations. In addition we offer mathematical proof for incidence of these bifurcations that take place in the considered system.

Keywords:

Two dimensional nuclear reactor dynamics , saddle-node , transcritical and pitchfork bifurcations , Sotomayor Theorem