Combining with the center manifold theorem, we calculated the stochastic Normal-Forms of a noisy Van der Pol-Duffing oscillator, and obtained the stochastic Normal-Forms on its center manifold.

Firstly,center manifold theorem and bifurcation theory are applied to prove the emergence of flip bifurcation in the system.

Let x~2+y~2+z~2=h(>0) be the first integral of the perturbed system,then the existence of limit cycles on the spherical surface was discussed by using averaging method and center manifold theory.

Based on the Hopf bifurcation theory, the nonlinear singularity phenomenon of low frequency oscillation is studied by means of center manifold theory in case the generator model is expanded to the fourth order and the excitation system operating parameters are changed.

The motion equations of submarine were reduced to a lower system which contains all dynamic properties of the original system by utilizing center manifold theory.

General programming method for calculating center manifold;

As to the model of a reactor, in which single group delayed neutron and power reactivity feedback are taken into account, it is judged that the model is unstable from dimension reducing by center manifold theory in this paper.

The high-dimensional system was transformed into a lower-dimensional one by center manifold theorem.

The centre manifold theory is used to reduce dimensions of the system.

The theory of centre manifold is first used to reduce the flutter system to a two-dimensional one.

With the use of centre manifold and dynamic system theory, the necessary and sufficient conditions are obtained for the solvabilities of the output regulator problems for the general nonlinear discrete_time system.