IEEE Circuits and Systems Magazine - Q3 2019 - 7

Abstract
Collective behaviors in multi-agent systems (MASs) is one of
the most ubiquitous phenomena in the natural world, which often exhibit through social interactions among their agents. It
is very important to understand the theoretical mechanisms at
the basis of different collective behaviors. Therefore, various
techniques and methods have been developed and investigated against this issue over the last decades. In this paper,
we concentrate on several models of collective behaviors in
bird flocks, a representative kind of MAS. Moreover, this article
aims at providing a discussion of various facets of this interdisciplinary field, including simulation models, mathematical
methods and control theory. The purposes are to offer readers
a better understanding of complex systems and to promote this
emerging topic on MASs.

I. Introduction
uman beings have always been fascinated by collectively moving animals that display a variety of
eye catching motion patterns in the natural world,
such as a school of fish [1], a herd of land animals [2], or a
flock of birds [3]. All of these can be generalized as multiagent systems (MASs), which are systems composed of
multiple interconnected autonomous agents. Owing to different types of social interactions among their agents, MASs
may present diverse collective behaviors. It is interesting
and actually crucial to deeply understand the underlying
mechanisms of the intriguing collective behaviors since
they are destined to bring great advantages to deal with
actual situations. Of specific interest, in this article, we will
focus on collective behaviors through social interactions
of bird flocks for simplicity and typicality.
The organized flight of birds has captivated and mystified observers and investigators since the very beginning when written history of nature appears. However,
this phenomenon is easy to observe but challenging to
characterize. In the 1930s, an ornithologist named Edmund Selous made a series of observations on various
species of birds over their collective motion, such as making abrupt turnings simultaneously when they are flying
in flocks. Because of lacking analysis technology, he even
hypothesized that these motions result from the telepathy within the flocks [4]. Subsequently, literatures with
respect to bird flocks have grown substantially, many
researchers and investigators have turned to theoretical
interpretations based on social interactions among birds.
Most recently, Vicsek et al. provided an excellent review

Digital Object Identifier 10.1109/MCAS.2019.2924507
Date of publication: 13 August 2019

of the state of the art regarding the observations and the
basic laws of collective motion behaviors [5].
In 1974, Heppner divided patterns formations of bird
flocks in flight into two categories: Line formations and
Cluster formations [6]. The former formations are generally demonstrated by large birds, such as geese or waterfowl, while the latter ones are usually composed of
relatively small birds, such as starlings or pigeons [6].
One interesting scientific question is: why geese fly in
a V while starlings fly in a cluster? The other interesting
question is: What might be the advantage of birds flying in
configurations corresponding to their body sizes? Perhaps
the answers are energy expenditure can be reduced
and orientation for collective motion can be enhanced
through social interactions within flocks when the birds
are flying at an optimal spacing [7]-[11]. Furthermore,
Hemelrijk and Hildenbrandt investigated some causes
of the variable shapes of bird flocks in 2011, they confirmed that flock size, interaction partner number and
turning sharpness, all these factors result in the variability of flock shape [12].
All birds are considered equal in the flocking formation models mentioned above, in which the birds can
only obtain information from neighbors. However, animal flocks with which we are familiar may not behave
in this way. For example, ants in a colony usually can
be separated into worker ants, soldiers, drones and the
queen, all which refer to the division of labor. So do the
bird flocks. Considering the behavior of birds flocking,
the most common division of roles is the leader-follower
mode. However, Leadership is not an inherent quality
that shows directional locomotion in flocking, there are
other situations that may be responsible for the emergence of leadership in bird flocks, such as foraging [3],
homing [13]-[16], obstacle and predator avoidance
[17]-[18], and landing [19]. The labor division of bird
flocks may not simply divide them into two categories,
that is, leaders and followers, the relationship among
them can be more sophisticated. In 2010, Nagy et al.
introduced the first hierarchical networked leader-follower model, which is instructive for further research
on leader-follower behaviors in bird flocks [20].
Collective decision making in biological systems is the
initial stage of collective behaviors. Bird flocks often need
to make common decisions or deliver information because it is crucial to their fitness and safety, for example,
which activities to perform, when to turn and in what
direction, where to forage or if they obey despotism or
democracy within the group [21]. However, information

J. Lü (email: jhlu@iss.ac.cn). Xiong Wang is with the School of Mathematics, Northwest University, Xi'an 710127, China. Jinhu Lü is with the School of
Automation Science and Electrical Engineering, State Key Laboratory of Software Development Environment, and Beijing Advanced Innovation Center
for Big Data and Brain Computing, Beihang University, Beijing 100191, China.
THIRD QUARTER 2019

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IEEE Circuits and Systems Magazine - Q3 2019

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