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This task allows subjects to make personality trait inferences and to associate these with the person on the corresponding portrait.
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This means that the potential curve has two pits and a hump and the corresponding phase portrait has obviously two centers and saddle equilibrium state on the phase portrait of (32).
The corresponding phase portrait of system (1) with (tau=10), is shown in Figure 2. Figure 2 Phase portraits of the model system ( 1 ).
The corresponding phase portrait (( u ),( {{{text{d}}u} mathord{left/ {vphantom {{{text{d}}u} {{text{d}}zeta }}} right. kern-0pt} {{text{d}}zeta }} )) is shown Fig. 2 and it obviously has two centers and saddle equilibrium state on the phase portrait of Eq. (16).
In "Planar dynamical system and phase portraits" section, we obtain a planar dynamical system and corresponding phase portraits.
The corresponding phase portraits for various values of h are showed in Figure 3. Figure 3 The phase portraits of model ( 2 ) for different values of h corresponding to Figure 1 and Figure 2.
In these bifurcation analyses, the nonlinear chatter behaviors of the present grinding system are examined and discussed through the resulting bifurcation diagrams of limit cycles, the Bautin bifurcation diagram, and the corresponding phase portraits.
The first one shows the Hopf bifurcation diagrams and the corresponding phase portraits of model (2) to confirm the above theoretical analysis, and it indicates new interesting complex dynamical behaviors.
Using the Poincaré portrait corresponding to non-autonomous systems, dynamic behavior of the mechanism is shown in discrete space, which is the criterion for the detection of chaos.
Figure 2 The phase portraits corresponding to Figures 1 (a) and (b).
The phase portraits corresponding to Figure 2(a) are shown in Figures 2(d - f) for showing eleven- and - f-coexisting chaotic attractors at (d = 3.58) and 3.72 and a chaotic attractor at (d=3.8).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com