Aplication of Hopf bifurcation theory and variational methods to the study of limit cycles in boiling water reactors

Abstract

In this paper we analyze the limit cycles which arise in Boiling Water Reactor using Hopf bifurcation theory and variational methods. We prove that we can apply the central manifold method to this kind of system in order to reduce the dimension of the state space. This systematic reduction is performed for the BWR dynamical system and it is obtained a reduced two dimensional one which contains all the information about the bifurcation. We have also introduced in this paper the parameter which define from a nonlinear point of view, the limit cycle stability. Finally the calculation of the limit cycle period is performed by variational and Hopf bifurcation methods, the agreement between both methods is excellent.