Complex BWR dynamics from the bifurcation theory point of view

Highlights: • There are BWR stability states which can be explained only in terms of nonlinear dynamics. • Hopf–Hopf bifurcations have been found in the neighborhood of a real BWR state. • The complex dynamics in the neighborhood of a Hopf–Hopf bifurcation is discussed. - Abstract: In a recently published (motivation) paper Lange et al., 2013 we analysed the BWR mode oscillation phenomenon from the bifurcation theory point of view. We demonstrated that some stability properties can be explained only in terms of nonlinear dynamics. In the present paper we shall continue the application of elements of the nonlinear stability analysis and analyse stability states which are characterized by the existence of simultaneous Hopf bifurcations (so-called Hopf–Hopf-bifurcations). From the bifurcation theory it is well-known that the solution manifold of the DEs describing the BWR dynamics can be surprisingly extensive in the vicinity of such bifurcation points. In the present paper we analyse the dynamics of a real BWR and search for a Hopf–Hopf point by appropriate parameter variation. The objective of this paper is to investigate and demonstrate the system dynamics which we have to expect if a Hopf–Hopf bifurcation exists. In a future paper we will analyse these different stability states reflecting the solution manifold near a Hopf–Hopf point concerning their technical relevance