Sentence examples for by using normal forms from inspiring English sources
Nevertheless, some elementary types of nonlinear behavior of control systems can be classified by using normal forms.
In Section 3, we derive the direction and stability of the Hopf bifurcation by using normal form method and central manifold theorem.
As far as we know, there are essentially three differential ways of obtaining Lyapunov constant for nilpotent critical points in theory: by using normal form theory [14], by computing the Poincaré return map [15] or by using Lyapunov functions [16].
In Section 3 we prove the existence of Neimark-Sacker and period doubling (flip) bifurcation for this system by analysing the characteristic equation, and then in Section 4 we investigate the direction of this bifurcations by using normal form theory. Finally in Section 5 we give numerical simulations to support our theoretical analysis.
Further more we prove the existence of Neimark-Sacker and period doubling (flip) bifurcation for this system by analysing the characteristic equation, and investigate the direction of this bifurcations by using normal form theory. Finally some numerical simulations are carried out to support the analytical results.
Also the dynamic behaviors of the system are investigated, by using normal form theory, center manifold theorem and bifurcation theory, it is shown that the system undergoes a Neimark Sacker bifurcation and a flip bifurcation, on varying step-size in some range.
Following [ 17, 27] (see also [ 28]) we analyse equations (25 - 26 25 - 26witherep = 0 and D v = 1) by using normal form analysis to approximate it by one of λ- ω type near the Hopf bifurcation.
The vibrations in the horizontal and vertical directions are analyzed on the center manifold near the double-zero degenerate point by using normal-form method.
By using the normal form theory and center manifold reduction for PFDEs developed by [23].
