IEEE Circuits and Systems Magazine - Q3 2019 - 10

birds, one can also explore the mysteries of V-like formations of birds [38].
More recently, the distinctive V-like formations of birds
still intrigued investigators and attracted researchers
to explore it further. For example, in 2008, Nathan and
Barbosa developed a comprehensive computer model
which can be applied to simulating the V-like formations
of birds [40]. In 2009, Hayakawa proposed a nonlinear
wave propagative model and performed a spatiotemporal analysis of the V-like formations [41]. In 2014, Portugal
et al. demonstrated that birds would show wingtip path
coherence when flying in V-like formations, in contrast,
when one bird flies behind another bird, there will be
no wingtip path coherence [42]. In order to investigate
which bird will fly in front when a social dilemma arises,
Voelkl et al. studied the behaviors of V-like formation
flock of juvenile Northern bald ibis, and showed that for
each individual, the length of flight time as a leader is
closely related with the duration of time it can save from
flying behind another bird [43].
B. Cluster Formations
Over the last decades, investigators have devoted to the
study of cluster formations and made lots of achievements. In this section, some simulation models and
mathematical methods for cluster formations of MASs
are investigated.
1) Simulation Model
a) The Boid Model
Perhaps the first widely known flocking simulation
model is the Boid model [44]. To build a computer animation of flocking with the ability of supporting geometrical flight of agents moving in a three dimensional
environment, Reynolds added behaviors to his model.
Therefore, his bird-like agents called "boids," which
moved along different trajectories determined by their
own equations taking into account the following three
types of interaction rules [44] (as illustrated on Fig. 3):
1) Collision Avoidance: avoid collisions with nearby
flockmates.

(a)

(b)

(c)

Figure 3. Three types of interaction rules of the Boid model.
(a) Collision avoidance, (b) velocity matching, (c) flock centering
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IEEE CIRCUITS AND SYSTEMS MAGAZINE

2) Velocity Matching: attempt to match velocity with
nearby flockmates.
3) Flock Centering: attempt to stay close to nearby
flockmates.
The Boid model is governed by only a few parameters which are apt to adjust. This model simulated
flocks just like an elaboration of a complex system, with
the "boids" being the agents. And the computer animations of aggregate motion of bird flocks are much like
the natural ones, with the agent or bird implementing
its own navigation in a dynamic environment as an independent performer. By working independently, the
birds not only try to stay close to the center of mass
of the flock, but also try to avoid collisions with one
another in their environment.
However, because of the inaccurate coding of agents'
behavior in the Boid model, it is difficult to objectively
weigh whether the simulation results are valid. In 2003,
to bypass the previous difficulties, Bajec et al. proposed
a novel algorithm which used linguistic programming
based on the boids' decision process, composed of
common sense, unclear and even partially knowledge
of dynamics in their model, therefore, this algorithm
achieved better simulation results than the classical
Boid model [45]-[46].
The Boid model is obtained directly from the observation of natural flocks. It can be used to explain the
movement, aggregation and synchronization of the clusters, as well as reveal the essential relationship of these
phenomena. Thus Boid model plays a significant role in
the behavioral research of bird flocks.
b) The Zonal Interaction Model
Another famous flocking simulation model was established by Couzin et al. in 2002 [47]. Analogous to the
Boid model, this model can be categorized into different emergency collective motions in three dimensional
space based on a few parameters. However, the agents
of the new model obey different interaction rules and
thus have completely different simulation results. The
interaction rules in this model are as follows [47]:
1) Repulsion: at all times, agents attempt to maintain a certain or relatively minimum distance with
each other.
2) Alignment and attractive tendencies: if agents do
not perform the repulsion rule, they tend to align
their headings with their mates and to be attracted towards their neighbors.
In each updating time step, agents interact with each
other in their perception zone which is divided into
three non-overlapping behavioral regions, as illustrated
in Fig. 4. This three regions are zone of repulsion (zor),
zone of orientation (zoo) and zone of attraction (zoa),
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IEEE Circuits and Systems Magazine - Q3 2019

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