Sentence examples for using the local bifurcation from inspiring English sources

In [26], taking a as a bifurcation parameter and using the local bifurcation theory, we get that the positive solution ((u(s),v s))) bifurcates from the semitrivial solution ((0,theta)).

Results are explained by using the local bifurcation theory of maps.

Using the local Hopf bifurcation theorem in [21], we conclude that the connected component (C(P_{2}, tau^{j},frac{2pi}{omega^)) through ((P_{2}, tau^{j}, frac{2pi}{omega^)) in Σ is nonempty.

Here we list the local bifurcation result and some preliminary results in [14], which will be used in this paper.

By the global bifurcation theorem in [10], we can extend the local bifurcation positive solution to the global one.

We now proceed to extend the local bifurcation curves obtained in Theorem 1.1 by the global bifurcation theory of Rabinowitz [16] and its developed version in [17].

Use the local Agricultural Extension Service.

The saddle-node and the Hopf bifurcations just described are the local bifurcations in this unfolding, that is, the bifurcations changing the stability of fixed points.

Convective-mode interaction occurring in reaction-driven convection in a porous medium is analyzed using local bifurcation theory.

Next, we will give attention to recapitulating the conditions of the existence for a Neimark-Sacker bifurcation (discrete Hopf bifurcation) by using the bifurcation theorem [11, 12, 19].

In order to infer the parameters of the model using the inverse bifurcation method, we need to localize the tangent bifurcation points based on dose response measurements.