Evolution of the population of Microtus Epiroticus: the Yoccoz-Birkeland model
We study the discretized version of a dynamical system given by a model proposed by Yoccoz and Birkeland to describe the evolution of the population of Microtus Epiroticus on Svalbard Islands, see http://zipcodezoo.com/Animals/M/Microtus_epiroticus . We prove that this discretized version has an att...
Main Authors: | , , |
---|---|
Format: | Report |
Language: | unknown |
Published: |
arXiv
2011
|
Subjects: | |
Online Access: | https://dx.doi.org/10.48550/arxiv.1101.5543 https://arxiv.org/abs/1101.5543 |
id |
ftdatacite:10.48550/arxiv.1101.5543 |
---|---|
record_format |
openpolar |
spelling |
ftdatacite:10.48550/arxiv.1101.5543 2023-05-15T18:29:46+02:00 Evolution of the population of Microtus Epiroticus: the Yoccoz-Birkeland model Nieto, Juan José Pacifico, Maria José Vieitez, José Ladislau 2011 https://dx.doi.org/10.48550/arxiv.1101.5543 https://arxiv.org/abs/1101.5543 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Dynamical Systems math.DS FOS Mathematics 37M05, 37N25, 92D25 Preprint Article article CreativeWork 2011 ftdatacite https://doi.org/10.48550/arxiv.1101.5543 2022-04-01T14:34:08Z We study the discretized version of a dynamical system given by a model proposed by Yoccoz and Birkeland to describe the evolution of the population of Microtus Epiroticus on Svalbard Islands, see http://zipcodezoo.com/Animals/M/Microtus_epiroticus . We prove that this discretized version has an attractor Lambda with a hyperbolic 2-periodic point p in it. For certain values of the parameters the system restricted to the attractor exhibits sensibility to initial conditions. Under certain assumptions that seems to be sustained by numerical simulations, the system is topologically mixing explaining some of the high oscillations observed in Nature. Moreover, we estimate its order-2 Kolmogorov entropy obtaining a positive value. Finally we give numerical evidence that there is a homoclinic point associated with p. : 33 pages, 5 figures Report Svalbard Microtus epiroticus DataCite Metadata Store (German National Library of Science and Technology) Birkeland ENVELOPE(16.587,16.587,68.594,68.594) Lambda ENVELOPE(-62.983,-62.983,-64.300,-64.300) Svalbard |
institution |
Open Polar |
collection |
DataCite Metadata Store (German National Library of Science and Technology) |
op_collection_id |
ftdatacite |
language |
unknown |
topic |
Dynamical Systems math.DS FOS Mathematics 37M05, 37N25, 92D25 |
spellingShingle |
Dynamical Systems math.DS FOS Mathematics 37M05, 37N25, 92D25 Nieto, Juan José Pacifico, Maria José Vieitez, José Ladislau Evolution of the population of Microtus Epiroticus: the Yoccoz-Birkeland model |
topic_facet |
Dynamical Systems math.DS FOS Mathematics 37M05, 37N25, 92D25 |
description |
We study the discretized version of a dynamical system given by a model proposed by Yoccoz and Birkeland to describe the evolution of the population of Microtus Epiroticus on Svalbard Islands, see http://zipcodezoo.com/Animals/M/Microtus_epiroticus . We prove that this discretized version has an attractor Lambda with a hyperbolic 2-periodic point p in it. For certain values of the parameters the system restricted to the attractor exhibits sensibility to initial conditions. Under certain assumptions that seems to be sustained by numerical simulations, the system is topologically mixing explaining some of the high oscillations observed in Nature. Moreover, we estimate its order-2 Kolmogorov entropy obtaining a positive value. Finally we give numerical evidence that there is a homoclinic point associated with p. : 33 pages, 5 figures |
format |
Report |
author |
Nieto, Juan José Pacifico, Maria José Vieitez, José Ladislau |
author_facet |
Nieto, Juan José Pacifico, Maria José Vieitez, José Ladislau |
author_sort |
Nieto, Juan José |
title |
Evolution of the population of Microtus Epiroticus: the Yoccoz-Birkeland model |
title_short |
Evolution of the population of Microtus Epiroticus: the Yoccoz-Birkeland model |
title_full |
Evolution of the population of Microtus Epiroticus: the Yoccoz-Birkeland model |
title_fullStr |
Evolution of the population of Microtus Epiroticus: the Yoccoz-Birkeland model |
title_full_unstemmed |
Evolution of the population of Microtus Epiroticus: the Yoccoz-Birkeland model |
title_sort |
evolution of the population of microtus epiroticus: the yoccoz-birkeland model |
publisher |
arXiv |
publishDate |
2011 |
url |
https://dx.doi.org/10.48550/arxiv.1101.5543 https://arxiv.org/abs/1101.5543 |
long_lat |
ENVELOPE(16.587,16.587,68.594,68.594) ENVELOPE(-62.983,-62.983,-64.300,-64.300) |
geographic |
Birkeland Lambda Svalbard |
geographic_facet |
Birkeland Lambda Svalbard |
genre |
Svalbard Microtus epiroticus |
genre_facet |
Svalbard Microtus epiroticus |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1101.5543 |
_version_ |
1766213146055278592 |