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1
1
0.8
0.8
0.6
0.6
0.4
0.4
N i =10
N i =30
N i =50
N i =10
N i =30
N i =50
0.2
0.2
0
0
10 −3
10 −2
10 −1
10 0
10 1
10 −3
10 −2
10 −1
10 0
10 1
r
r
(a)
(b)
Fig. 17.7. Order parameter v a vs. for dierent values of N i and : = 0 (a) and = 1 (b).
Other parameters (except for N i ) are as in Fig. 17.6(a).
1
1
N i =10
N i =30
N i =50
N i =10
N i =30
N i =50
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
10 −3
10 −2
10 −1
10 0
10 1
10 −3
10 −2
10 −1
10 0
10 1
r
r
(a)
(b)
Fig. 17.8. Order parameter v d vs. for dierent values of N i and : = 0 (a); = 1 (b). Other
parameters (except for N i ) are as in Fig. 17.6(a).
6= 0. Thus in the latter case the group is able to follow the direction of informed
individuals for higher values of the density.
Similarly to Vicsek's model, we analyze the system behavior in presence of a
noise term, characterized by a Gaussian distribution with zero mean and stan-
dard deviation . Figure 17.9(a) shows that, when the noise level is increased, v a
decreases, as in Vicsek's model. Moreover, also in this case the introduction of
long-range connections improves the system performance (in terms of v a ) in the
presence of noise.
In Fig. 17.9(b) v d as a function of is shown for dierent values of . When the
noise level is increased, v d also decreases. It is worth noticing that in the case of
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