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Figure 15 Functional boxplot computed on a simulated toy example, corresponding to Model 2 in [ 19 ].

In fact, we see that for the continuous model corresponding to model (3) does not occur the bifurcation at the equilibrium (E^{ast}).

Temperature versus depth (or control volume number) profiles for the 63 simulated models were similar to the one presented in Figure 4 corresponding to model M55 (Table 2).

Figure 4 also shows the seismic ray traces of the S-wave, S and (S), corresponding to model D1 and D2, respectively, and travel times, 13.15 s and 14.12sat−6 km, are also marked on the velocity and traction change.

Moreover, by the results of [17], we find the interesting phenomenon that (E^{ast}) of the continuous model corresponding to model (3) is globally asymptotically stable if (bdelta> 1-alpha )(1-bdelta> 1-alpha

Figure 1a,b depicts the true correlation and complementary correlation functions of x t, Figure 1c,d the simulated simulated ones corresponding to model 1 and Figure 1e,f the simulated ones for model 2. We can see that the simulated trajectories of model 1 pick up adequately the behavior of the correlation function.

Motivated by a similar idea, we study the following discrete-time model corresponding to model (2): u ( t + 1 ) = u ( t ) exp [ 1 − u ( t ) − c v ( t ) u ( t ) + b ], v ( t + 1 ) = v ( t ) exp [ θ ( 1 − v ( t ) u ( t ) ) ], (3).

The result corresponding to Model 9 without the two outlier peptides are shown in Figure 7 (d).