In this paper we give a modified non-interior predictor-corrector path following algorithn for the NCP, and the global and local convergence analysis of the algorithm, at the end of this paper, there are numerical examples t.

By a newly developed method for finding the normal form, this paper deduces the normal form for the mutiple Hopf bifurcations of a high dimensional nonlinear dynamical system in noninternal resonance cases when its Jacobian matrix has many pairs of imaginary eigenvalues, and gives the expressions of the coefficients in the normal form by those inthe original system.