IEEE Circuits and Systems Magazine - Q3 2019 - 8

transfer and decision making in collective motion of
birds have long puzzled researchers. In 1999, Perera and
Guilford explored the social information transfer among
homing pigeons which were trained to forage within
an indoor arena, and discussed some possible ways of
spreading spatial information among birds [22]. In 2009,
List et al. developed an agent-based model for the case
of nest-site choice by bees, and showed that the bees'
decision making process stems from certain interplay
of interdependence and independence within them [24].
In 2010, combining a self-propelled particle system with
novel boundary conditions, Bhattacharya and Vicsek introduced a landing model of birds, and revealed that the
birds' decision intention from flying to landing would be
much sharper than usual [23]. In 2011, Bode et al. presented a model and analyzed the concerning factors

(a)

(b)
Figure 1. Two formations of bird flocks [130]-[131]. (a) Line
formation, (b) cluster formation.
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IEEE CIRCUITS AND SYSTEMS MAGAZINE

which affect the preference of decision making of moving birds [25]. Here we would like to note that Ref. [26]-
[28] are very useful reviews on these problems.
The state of the art of the research on bird flocks includes not only modeling descriptions, but also experimental observational studies. For example, an impressive
work was carried out by Cavagna et al. in Ref. [29]-[30].
In their project, researchers reconstructed the positions
of individual starlings in flocks composed of thousands
of birds, the data was analyzed via computer vision techniques. In 2008, Ballerini et al. measured the threedimensional position information of 2700 birds, and investigated the main features of bird flocks [31]. In 2012,
Kattas et al. established the first computational modeling methods which could be applied to inferring the
collective behavior of flocks by using the experimental
field data of pigeons [32]. In addition, by utilizing highprecision GPS, researchers obtained high resolution
spatial data in order to examine flocking behaviors more
closely. Typical examples are, using GPS tracking technology, in 2002, Biro et al. showed that the directional decisions of homing have been made before released [33].
In 2006, Biro et al. proposed that if the directional preference between two birds is less than a threshold, they
would average their routes, otherwise, one bird would
be the leader while the other would be the follower [34].
In 2008, by using GPS track analysis tool, Dell'Ariccia
discovered that flock flying improves pigeons' homing
behavior [35].
In this tutorial review article, we will briefly summarize collective behaviors of bird flocks through social
interactions among individuals from a multi-agent systems viewpoint. The rest of this article is arranged as
follows. Section II introduces some pattern formation
models based on different social interactions among
birds. Hierarchical networked group dynamics of communication within a flock is investigated in Section III.
Section IV gives the underlying mechanisms of collective decision making in biological moving systems and
control theory. Section V makes some concluding remarks, highlights its significance and lists some challenging future research problems.
II. Representative Formation Models Based
on Social Interactions
Preliminarily, some necessary notations which will be
used throughout this paper are listed as follows. Suppose bird flocks are composed of N individuals, let
I = {1, 2, f, N } be the set of these birds, unless otherwise stated, for every bird i ! I, at time t, its position
and heading are denoted by x i (t ) and i i (t ), respectively. And v i (t ) = v (cos i i (t ), sin i i (t )) represents the velocity of bird i (i ! I ) at time t, denote Tt is the time unit.
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IEEE Circuits and Systems Magazine - Q3 2019

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