Sentence examples for by applying bifurcation analysis from inspiring English sources

This study extends the analysis of the Pettigrew model by applying bifurcation analysis, singularity theory, and numerical simulation.

Finally in Section 3, we prove our main results Theorems 1.1 and 1.2 by applying bifurcation theory.

They proved the existence, multiplicity, and stability of positive solutions for the above problem by applying bifurcation techniques.

They proved the existence, multiplicity and stability of positive solutions for problem (1.5) by applying bifurcation techniques.

Recently, Ma et al. [18, 19] studied the existence of positive solutions for the periodic problems by applying bifurcation techniques.

The main idea is to apply numerical bifurcation analysis to the closed-loop process, using the controller tuning parameters, the set points, and parameters describing model uncertainty (parametric as well as unmodeled dynamics) as bifurcation parameters.

The core idea is to apply numerical bifurcation analysis to the closed-loop process, using the controller/observer tuning parameters, the set points, and parameters describing model uncertainty (parametric as well as unmodeled dynamics) as bifurcation parameters.

As an aspiring politician, I strive to improve society by applying statistical analysis to decision making.

Then, by applying the spectral analysis and the principle of exchange stability, we prove that the bifurcation solutions near the bifurcation points are locally asymptotically stable.

The determined conditions on bifurcation are very straightforward, detailed and impressive and simple to be verified in the present work by applying Hopf bifurcation theory.

By applying the bifurcation theorem of López-Gómez [[7], Theorem 6.4.3], we shall establish the following: Theorem 1.1.