Zero-Hopf bifurcation in continuous dynamical systems using multiple scale approach

An efficient scheme for studying multiparametric Zero-Hopf bifurcation is provided to extend A. Nayfeh multiple-time scale technique of codimension-one bifurcations. The suggested approach treats the cases of high codimension bifurcations successfully. Compared to the well-known averaging method, center manifold reduction method and projection method, the present approach is more simple and can be applied with less computational cost and high efficiency to a wider class of problems involving the cases where purely imaginary, zeros and negative real eigenvalues coexist simultaneously.