Sentence examples for properties of the Hopf from inspiring English sources

3, properties of the Hopf bifurcation are investigated.

Furthermore, the properties of the Hopf bifurcation such as direction and stability are determined.

Furthermore, properties of the Hopf bifurcation at the critical value (tau_{0}) are also investigated.

Explicit formulae for determining the properties of the Hopf bifurcation are derived in Section 3.

Section 3 is devoted to the properties of the Hopf bifurcation.

The purpose of this paper is to discuss the stability and the properties of the Hopf bifurcation of model (1.4).

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

In [20], Bianca et al. further studied an economic growth model with two delays and they investigated the existence and properties of Hopf bifurcation of the model by regarding the possible combination of the two delays as the bifurcation parameter.

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

According to the analysis of the properties of Hopf bifurcation in [22], we have the following results.

Second, by applying the normal form method and center manifold theorem, we investigate the properties of Hopf bifurcation, such as the direction and stability.