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The phase plane trajectory of the ray-based system can be periodic, quasi-periodic, and unstable.
Reference [16] proposed a transient instability detection criterion based on the geometric feature of phase plane trajectory.
Finally, the surface effects on the phase plane trajectory of fundamental mode time-dependent function have been shown.
Another benefit is that PEC signals are relatively easier to interpret, while it requires a special skill of the operators for interpreting conventional ECT signals which are presented in the impedance plane trajectory.
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Dynamic response of the system is presented in the form of phase plane trajectories, Poincare maps and time histories.
Phase plane trajectories traced out by the responses of the model to two different SEEs are plotted in Figs. 6a, c.
Phase plane trajectories, Poincaré maps and power spectral density diagrams are derived to illustrate both the symmetrical and asymmetrical chaotic vibrations.
Fig. 6 Phase plane trajectories traced out by the responses of the model to two different SEEs (panels a and c) and the SEEs profiles (top) and the corresponding voltage responses (bottom) (panels b and d).
Here harvesting efforts lie in the region α > 2 ( 1 + E 1 ) x ∗ 3 x ∗ 2 − 1 > [ 3 A β + 11 ( 1 + E 1 ) ] x ∗ 3. Figure 2 Phase plane trajectories corresponding to different initial levels ( E 1 = 2, E 2 = 1.5 ).
Phase plane trajectories, resonance curves and stability limit of the solutions are obtained and compared with the results of numerical integration in order to examine the validity of the present analysis.
In total 34 bifurcation diagrams were obtained, each of which had different dynamic features and some of which showed the maximum 17 different behaviors of phase plane trajectories for a range of the Damköhler number.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com