Sentence examples for method and center from inspiring English sources

We apply the normal form method and center manifold theorem to obtain the direction and stability of the Hopf bifurcation.

The way to do this is the combination of the normal form method and center manifold theory in [22].

Furthermore, the properties of the Hopf bifurcation are determined by using the normal form method and center manifold theory.

We determine the Hopf bifurcation direction and the properties of these bifurcating periodic solutions by using the normal form method and center manifold theorem.

In Section 3, the properties of the Hopf bifurcation such as the direction and stability are determined by using the normal form method and center manifold theorem.

The direction of the Hopf bifurcations and the stability of bifurcating periodic solutions are determined by using the normal form method and center manifold theory.

Extensions of the asynchronous time integration to Runge Kutta method and centered schemes are given.

Further, the properties of Hopf bifurcation are studied by using the normal form method and the center manifold theorem.

Furthermore, we use the normal form method and the center manifold theorem to determine the direction of the Hopf bifurcation and the stability of the bifurcated periodic solutions.

Explicit formulas determining the properties of a Hopf bifurcation are obtained by using the normal form method and the center manifold theorem.

By using the normal form method and the center manifold theory, we derive the explicit formulas for determining the direction and stability of Hopf bifurcation.