Sentence examples for using the phase plane from inspiring English sources

The frequency response is obtained by the harmonic balance method, and its stability is investigated using the phase plane method.

In this paper, we propose a new fuzzy controller using the phase plane, in order to improve the overall performance of the fin servo system.

The stability and convergence property of this ANF is studied using Lyapunov method and is also analysed graphically using the phase plane technique to understand its behaviour and convergence properties under different conditions.

The standard hemodynamic indexes of LV systolic and diastolic function derived from the time-dependent LV pressure contour could be easily obtained using the phase plane method.

A possible way for us is to use the phase-plane analysis and topological degree methods, also used in [12], and give the following fundamental hypotheses.

To use the phase-plane analysis and topological degree methods, we embed (1.1) into a family of equations with one parameter (lambdain[0,1]), x"+frac{1}{4}n^{2}x+(1- lambda) biggl -1-frac{1}{x^{3}}biggl -1-frac{1}{igl(x(t),x(t-tau) biggl -1-frac{1}{).

Systems of DEs and the phase plane are used to model competition, predator prey interactions, and epidemics.

Instead, we shall use Poincaré maps for the orbits in the phase plane that determined by the dynamics of eq. 3 with the control of eq. 7.

The stability analysis of the first controller is carried out by using the standard tools of linear control systems, whereas the analysis of the intermittent controllers is based on the use of Poincaré maps defined in the phase plane.

The required phase hologram is calculated using a weighted Gerchberg-Saxton algorithm [ 21] that assumes a fixed amplitude profile in the phase plane and iteratively varies the phase hologram [ 20, 22].

Nonlinear oscillations and the phase plane.