コロキウム

The codimension-two fold-Hopf bifurcation is a fundamental and important behavior in dynamical systems and has been extensively studied. At the bifurcation point, the linearized vector field has a zero eigenvalue and a pair of purely imaginary eigenvalues, and fold (i.e., saddle-node) and Hopf bifurcation curves meet. In this talk we consider the normal form of the fold-Hopf bifurcation and prove its meromorphic nonintegrability in the meaning of Bogoyavlenskij for almost all parameter values. Our proof is based on a generalized version of the Morales-Ramis theory for non-Hamiltonian systems and related variational equations up to second order are used.