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THE PHILLIP ISLAND PENGUIN PARADE (A MATHEMATICAL TREATMENT)

Part of: Applications - Dynamical systems and ergodic theory Mathematical biology in general

Published online by Cambridge University Press:  08 August 2018

SERENA DIPIERRO Open the ORCID record for SERENA DIPIERRO [Opens in a new window] ,
LUCA LOMBARDINI Open the ORCID record for LUCA LOMBARDINI [Opens in a new window] ,
PIETRO MIRAGLIO Open the ORCID record for PIETRO MIRAGLIO [Opens in a new window]  and
ENRICO VALDINOCI Open the ORCID record for ENRICO VALDINOCI [Opens in a new window]
SERENA DIPIERRO*
Affiliation:
Dipartimento di Matematica, Università degli Studi di Milano, 20133 Milan, Italy email serena.dipierro@unimi.it School of Mathematics and Statistics, University of Western Australia, Crawley, WA 6009, Australia
LUCA LOMBARDINI
Affiliation:
Dipartimento di Matematica, Università degli Studi di Milano, 20133 Milan, Italy email serena.dipierro@unimi.it Faculté des Sciences, Université de Picardie Jules Verne, 80039 Amiens CEDEX 1, France email luca.lombardini@unimi.it
PIETRO MIRAGLIO
Affiliation:
Dipartimento di Matematica, Università degli Studi di Milano, 20133 Milan, Italy email serena.dipierro@unimi.it Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, 08028 Barcelona, Spain email pietro.miraglio@unimi.it
ENRICO VALDINOCI
Affiliation:
Dipartimento di Matematica, Università degli Studi di Milano, 20133 Milan, Italy email serena.dipierro@unimi.it Istituto di Matematica Applicata e Tecnologie Informatiche, 27100 Pavia, Italy email enrico@mat.uniroma3.it School of Mathematics and Statistics, University of Melbourne, Parkville, Vic. 3010, Australia School of Mathematics and Statistics, University of Western Australia, Crawley, WA 6009, Australia
*
✉serena.dipierro@unimi.it
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Abstract

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Penguins are flightless, so they are forced to walk while on land. In particular, they show rather specific behaviours in their homecoming, which are interesting to observe and to describe analytically. 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 eyesight of the penguins and their cruising speed. The model that we propose favours the formation of conglomerates of penguins that gather together, but, on the other hand, it also allows the possibility of isolated and exposed individuals.

The model that we propose is based on a set of ordinary differential equations. Due to the discontinuous behaviour 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 remain isolated). To facilitate the intuition of the model, we also present some simple numerical simulations that can be compared with the actual movement of the penguin parade.

Keywords

population dynamicsEudyptula minorPhillip Islandmathematical models

MSC classification

Primary: 92B05: General biology and biomathematics
Secondary: 92B25: Biological rhythms and synchronization 37N25: Dynamical systems in biology
Type
Research Article
Information
The ANZIAM Journal , Volume 60 , Issue 1 , July 2018 , pp. 27 - 54
Copyright
© 2018 Australian Mathematical Society 

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