Information Technology Reference
In-Depth Information
orientation and attraction tasks are performed concurrently as
d
ti
(t + t) =
d
oi
(t + t) + d
ai
(t + t)
2
:
(17.6)
As stated above, informed agents have a preferential direction to pursue. In-
formed agents act on the basis of a combination of their individual criterion (i.e.,
the preferential direction), with the social criteria described above (i.e., avoidance,
orientation and attraction tasks). Also for informed agents, the avoidance task has
the highest priority and is performed in an exclusive fashion, and is modeled as in
Eq. (17.3). The behaviour of an informed agent, not engaged in an avoidance task,
is modeled as
d
ti
(t + t) + !g
jd
ti
(t + t) + !gj
d
0
ti
(t + t) =
(17.7)
where g is the preferential direction vector, ! regulates the balance of individual
and social criteria, and d
ti
(t + t) is computed as in Eq. (17.6).
The aim of Couzin's work is not limited to assessing the ability of the collective
to move along a spontaneously emerging direction, as in [Vicsek et al. (1995)].
Besides this, the interest is also focused on the ability of the group to move along
the direction of the informed individuals. Therefore, the parameter expressed in
Eq. (17.2) is not sucient to evaluate the eectiveness of the leadership of the
informed elements in guiding the group towards their preferential direction. This
ability can be quantied through the parameter v
d
, which is dened as
v
d
= 1L
avg
(17.8)
where L
avg
is the angle between the average direction of all the agents, and the
preferential direction, normalized between 0 and 1. L
avg
is computed as
P
N
j=1
v
j
(t)
jv
j
(t)j
1
N
g
L
avg
=
(17.9)
where g is the preferential direction. It is clear that v
d
is closer to 1 as long as
all the agents tend to move closer to the preferential direction. On the contrary,
v
d
approaches zero when all the agents tend to move opposite to the preferential
direction.
The results obtained by Couzin's and co-workers can be summarized in the
following points:
For a given group size the accuracy of the collective direction of motion with
respect to the preferential direction increases asymptotically as the proportion
of informed individual increases.
As the group size increases, a smaller proportion of informed individuals is
needed to achieve a given degree of coordination (i.e. a value of parameter v
d
).
This means that for big groups, only a few experienced elements are needed to
guide the group towards the preferential direction.
