Bifurcation to quasi-periodic tori in the interaction of steady state and Hopf bifurcations

Scheurle, J. and J. E Marsden

SIAM J. Math. Anal., 15, (1984), 1055-1074

Abstract:

Bifurcations to quasi-periodic toil in a two parameter family of vector fields are studied. At criticality, the vector field has an equilibrium point with a zero eigenvalue and a pair of complex conjugate eigenvalues. This situation has been studied by Langford, Iooss, Holmes and Guckenheimer. Here we provide explicitly computed conditions under which the stability of the secondary branch of toil, and whether the flow on them is quasiperiodic, can be determined. The results are applied to "Brusselator" system of reaction diffusion equations.