![](bg7.png)
Figure 5: Trajectories for β and g optimal, with N
d
= 3
doors, under different conditions for the position/width of
the doors.
5 CONCLUSIONS
It is a true challenge, to analytically discuss the swarm
dynamics of heterogeneous interacting agents. Due to
heterogeneity, ordinary analytical tools like the mean-
field approach are to be ruled out a priori. Hence be-
sides simulation experiments, very little hope remains
for rigorous theoretical results. We think particularly
to modeling approaches relying on statistical mechan-
ics and phase transitions to explain the emergence of
self-organized spatio-temporal patterns (i.e flocking).
Howeveras ourpaper intends to show, facing inhomo-
geneous swarms problems, complete hope for analyt-
ical results should not be abandoned. The theoretical
analysis, when achievable, definitely offers sources of
inspiration for new and unexpected research axis.
In our present contribution, we barely scratched
the wealth of analytical possibilities. Indeed, swarm
heterogeneity has numerous origins, affecting the in-
dividual drifts and/or the variances, modeling the sen-
sitivity of each agent to the external random environ-
ment. In parallel, heterogeneity can either be sys-
tematic, thus implying that each agent behaves dif-
ferently, or can be limited to one or only a few indi-
viduals who exhibit singular behaviors. In the latter
configuration, the emergent swarm dynamics can be
affected, sometimes even strongly, by the exotic be-
havior of this (or these) individual(s). The influence
of the exotic fellow(s) can hence be viewed as a soft
control mechanism, either harmful or beneficial. The
exotic insiders, acting as leaders (or as shills in econ-
omy) are not detected to be singular by the other fel-
lows, offering the (politically frightening possibility!)
to drive large swarms towards global goals known
only to the manipulators. A formal analytical ap-
proach (complemented with simulations) to this gen-
eral problematic is a truly fascinating challenge.
Further works include analysis of multiple shills
influence, leading to the separation of the initial
swarm into multiple flocks, one shill soft-controlling
each flock. Generalisation in two or three dimensions
would also provide more realistic applications.
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