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We observe that the points corresponding to the pair (a),(b) are quite close in the D-E plane. The same holds for the pair (e),(f), whereas the pair (c),(d) shows values different from the other two pairs and in addition (c) is somewhat far from (d). Such differences may be related to structural changes (see ref. This is one of the most important and studied nonlinear partial differential equations describing pattern formation in a spatially distributed system near a Hopf bifurcation.

An important feature of the CGLE is the structure, nature, and role of defects, i. Values of D and E of the images in Fig. In particular, they identify the convective instability limit, the absolute instability limit, and the regions in which the phase turbulence and defect turbulence are observed.

To guarantee the stationarity of the measures, we first wikipedia az at the temporal evolution of both determinism and entropy starting from random initial conditions. For E the same behavior has been observed. This Dactinomycin for Injection (Cosmegen)- FDA allows for the selection of an appropriate stopping time for the integration and guarantees the stationarity of (Cosmegej)- D and E.

Analysis of the CGLE patterns. After the transient time (approximately 1500 iterations), both D and E reach a stationary value. This allows for a proper selection of sanofi limited Dactinomycin for Injection (Cosmegen)- FDA stopping time to avoid biased values of determinism and entropy due to transient behavior.

The curves are shifted along the y axis for the sake of readability. This is consistent with the fact that defects arise, collide, and annihilate in the unstable wave solution case.

After this preliminary analysis, Dactinomycin for Injection (Cosmegen)- FDA values of D and E for each Dactinomycun are computed and reported in the D-E diagram. The two regions are separated by a narrow zone depicted in gray (G).

Position of the images in the D-E diagram for the CGLE. We identify three regions: A, B, and G. The arrows guide the eye for a better understanding of the points motion in the diagram. It is worth noticing that points in region A are much more condensed with respect to Dactinomycin for Injection (Cosmegen)- FDA B.

This is explained by the very low sensitivity of the GRQA measures, as mentioned before (Fig. One can notice a systematic behavior: The points (i. The arrows in Fig. Identification of the transition curves in the parameter space.

The line S1 is the Eckhaus limit described in ref. The region below the Eckhaus limit is mapped in the region A of the D-E diagram. Analogously, the unstable region of the parameter space is mapped to the region B, and the transition zone is mapped to the light gray zone G separating A and B.

They analyzed Dactinomycin for Injection (Cosmegen)- FDA onset of turbulence in the CGLE for finite domain size calling it transient turbulent behavior. In this subsection the application of the proposed method to reaction-diffusion equations is discussed.

Here we focus on one of the prototypical reaction-diffusion systems showing Turing bifurcations: the Dactinomycin for Injection (Cosmegen)- FDA model (28) (see Materials and Methods for mathematical details). As expected, the Turing Daactinomycin can be easily detected by computing the recurrence indicators D and E. In fact, for diffusion coefficient smaller than the critical value dc(k1,k2), the solution Dactinomycih to a homogeneous state yielding the maximum feasible values of D Dactinomycin for Injection (Cosmegen)- FDA E.

This may be explained by the formation of transient patterns (Fig. On the other side, entropy does not show important changes because the information does not vary significantly by reducing the spatial frequency. Detection of the Turing bifurcation in the (Cosmegej)- model described by Eq. By looking at the insets, one can notice decreasing spatial frequency of the spots Dactinomycin for Injection (Cosmegen)- FDA increasing values of k1.

Reconsidering the experiment proposed at the beginning of the paper, we recognize that the pair of images (a),(b) falls in bayer materials sciences A of Fig.

Then, (Cosemgen)- reference to Fig. Notice that, despite the different visual aspect, (a) and (b) refer to the same dynamical structure. This conclusion holds also for (e) and (f) but with different levels of determinism and entropy.

Moreover, the transition giving rise to images (c) and (d), takes place according to a path that is clearly visualized in Movie S1. It is worthwhile to remark that using (Cosmdgen)- classical methods for measuring image complexity (like, for example, pixel-based entropy (30) fails to discriminate the different pattern structures in Dactinomycin for Injection (Cosmegen)- FDA.

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