Chaos in Ecology: The Topological Entropy of a Tritrophic Food Chain Model
An ecosystem is a web of complex interactions among species. With the purpose of understanding this complexity, it is necessary to study basic food chain dynamics with preys, predators and superpredators interactions. Although there is an elegant interpretation of ecological models in terms of chaos...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2008/541683 |
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| author | Jorge Duarte Cristina Januário Nuno Martins |
| author_facet | Jorge Duarte Cristina Januário Nuno Martins |
| author_sort | Jorge Duarte |
| collection | DOAJ |
| description | An ecosystem is a web of complex interactions among species. With the purpose of understanding this complexity, it is necessary to study basic food chain dynamics with preys, predators and superpredators interactions. Although there is an elegant interpretation of ecological models in terms of chaos theory, the complex behavior of chaotic food chain systems is not completely understood. In the present work we study a specific food chain model from the literature. Using results from symbolic dynamics, we characterize the topological entropy of a family of logistic-like Poincaré return maps that replicates salient aspects of the dynamics of the model. The analysis of the variation of this numerical invariant, in some realistic system parameter region, allows us to quantify and to distinguish different chaotic regimes. This work is still another illustration of the role that the theory of dynamical systems can play in the study of chaotic dynamics in life sciences. |
| format | Article |
| id | doaj-art-f4a7460cba1a4083a863ed27106c3ea8 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-f4a7460cba1a4083a863ed27106c3ea82025-02-03T05:47:44ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2008-01-01200810.1155/2008/541683541683Chaos in Ecology: The Topological Entropy of a Tritrophic Food Chain ModelJorge Duarte0Cristina Januário1Nuno Martins2Department of Chemistry, Mathematics Unit, ISEL-High Institute of Engineering of Lisbon, rua Conselheiro Emídio Navarro 1, 1959-007 Lisbon, PortugalDepartment of Chemistry, Mathematics Unit, ISEL-High Institute of Engineering of Lisbon, rua Conselheiro Emídio Navarro 1, 1959-007 Lisbon, PortugalDepartment of Mathematics, Centre of Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico (IST), Technical University of Lisbon, rua Rovisco Pais 1, 1049-001 Lisbon, PortugalAn ecosystem is a web of complex interactions among species. With the purpose of understanding this complexity, it is necessary to study basic food chain dynamics with preys, predators and superpredators interactions. Although there is an elegant interpretation of ecological models in terms of chaos theory, the complex behavior of chaotic food chain systems is not completely understood. In the present work we study a specific food chain model from the literature. Using results from symbolic dynamics, we characterize the topological entropy of a family of logistic-like Poincaré return maps that replicates salient aspects of the dynamics of the model. The analysis of the variation of this numerical invariant, in some realistic system parameter region, allows us to quantify and to distinguish different chaotic regimes. This work is still another illustration of the role that the theory of dynamical systems can play in the study of chaotic dynamics in life sciences.http://dx.doi.org/10.1155/2008/541683 |
| spellingShingle | Jorge Duarte Cristina Januário Nuno Martins Chaos in Ecology: The Topological Entropy of a Tritrophic Food Chain Model Discrete Dynamics in Nature and Society |
| title | Chaos in Ecology: The Topological Entropy of a Tritrophic Food Chain Model |
| title_full | Chaos in Ecology: The Topological Entropy of a Tritrophic Food Chain Model |
| title_fullStr | Chaos in Ecology: The Topological Entropy of a Tritrophic Food Chain Model |
| title_full_unstemmed | Chaos in Ecology: The Topological Entropy of a Tritrophic Food Chain Model |
| title_short | Chaos in Ecology: The Topological Entropy of a Tritrophic Food Chain Model |
| title_sort | chaos in ecology the topological entropy of a tritrophic food chain model |
| url | http://dx.doi.org/10.1155/2008/541683 |
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