- 16-94 Serena Dipierro, Luca Lombardini, Pietro Miraglio, Enrico Valdinoci
- The Phillip Island penguin parade
(a mathematical treatment)
Nov 26, 16
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Abstract. We present a simple mathematical formulation to
describe the little penguins parade in Phillip Island.
We observed that penguins have the tendency
to waddle back and forth on the shore to create
a sufficiently large group and then walk home compactly together.
The mathematical framework that we introduce describes
this phenomenon, by taking into account
``natural parameters'', such as the sight of the penguins,
their cruising speed and the possible ``fear'' of animals. On the one hand,
this favors the formation of rafts of penguins
but, on the other hand, this may lead to the panic of isolated and exposed
The model that we propose is based on a set
of ordinary differential equations. Due to the discontinuous
behavior of the speed of the penguins, the mathematical
treatment (to get existence and uniqueness of
the solution) is based on a ``stop-and-go'' procedure.
We use this setting to provide rigorous examples in which
at least some penguins manage to safely return home (there are also cases
in which some penguins freeze due to panic).
To facilitate the intuition of the model,
we also present some simple numerical simulations
that can be
compared with the actual movement of the penguins parade.