Rigorous verification of cocoon bifurcations in the Michelson system

Abstract

We prove the existence of cocoon bifurcations for the Michelson system where and is a parameter, based on the theory given in (Dumortier et al 2006 Nonlinearity 19 305–28). The main difficulty lies in the verification of the (topological) transversality of some invariant manifolds in the system. The proof is computer-assisted and combines topological tools including covering relations and the smooth ones using the cone conditions. These new techniques developed in this paper will have broader applicability to similar global bifurcation problems.