Information Technology Reference
In-Depth Information
mechanisms of adjustment of the individual directions of motion, according to the
distance from its neighbors.
As we did with Vicsek's model, let us summarize in few points the rules which
govern the evolution of the model which is, also in this case, discrete in time and
continuous in space:
(1) The highest priority task for individuals is to avoid collisions within a repulsion
radius, r
r
, thus maintaining their vital space [Krause and Ruxton (2002)].
(2) If individuals are not busy in performing the avoidance task, they tend to align
with closer neighbors, contained within a given orientation radius r
o
(this is in
fact the governing rule in Vicsek's model [Vicsek et al. (1995)]).
(3) Together with orientation, individuals tend to approach neighbours [Partridge
and Pitcher (1980); Partridge (1982a)] which are out of the orientation radius
and within an attraction radius r
a
.
For dierent values of its parameters, this model is able to reproduce dierent
types of collective behaviors such as:
swarm, i.e. a compact group with low level of parallel alignment and low angular
momentum, observed in insects [Okubo and Chiang (1974); Ikawa and Okabe
(1997)] and sh schools [Pitcher and Parrish (1993)];
torus formation, in which individuals rotate around an empty core, observed in
sh schools in open water [Parrish and Edelstein-Keshet (1999)];
parallel group, in which the individuals move with highly aligned arrangement
and low angular momentum, observed in bird ocks and sh schools [Major and
Dill (1978); Partridge (1982b)].
Couzin et al. [Couzin et al. (2005); Couzin (2006)] formulated a further model
which includes the presence of experienced individuals, who have a preferential
direction of motion. This is motivated by the fact that there exist in nature examples
in sh schools where a minority of individuals can inuence the foraging activity of
the group [Reebs (2000)]. It has also been observed that in honeybee swarms very
few individuals can lead the group to a new nest site [Seeley (1985)]. The existence
and the role of experienced individuals in animal collectives is discussed in more
depth in [Couzin et al. (2005)] and in the references in there.
The presence of informed individuals is taken into account in the model with a
further rule:
(4) There exist a number of informed individuals, who move by mixing a social
criterion (emerging from rules 2 and 3), and an individual one, that is moving
in the preferential direction.
Let us review the model in more detail. As for Vicsek's model, N agents move
in a continuous 2D space of linear dimension L, with periodic boundary conditions.
