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Quantifying chaos for ecological stoichiometry

Source: Chaos 20, 033105 (2010); doi:10.1063/1.3464327

Published 23 July 2010

KEYWORDS and PACS
Keywords
PACS
  • 05.45.Gg
    Control of chaos, applications of chaos
  • 89.75.-k
    Complex systems
  • 87.23.Cc
    Population dynamics and ecological pattern formation
  • YEAR: 2010
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PUBLICATION DATA
ISSN:
1553-9628 (online)
Publisher:
AIP is a member of CrossRef AIP
Jorge Duarte,1,2,3 Cristina Januário,1,3 Nuno Martins,2,3 and Josep Sardanyés3,4
1Department of Chemistry, Mathematics Unit, ISEL-High Institute of Engineering of Lisbon, Rua Conselheiro Emídio Navarro 1, 1949-014 Lisboa, Portugal
2Departamento de Matemática, Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
3Dynamical Systems and Complexity (DySCo) Group, Rua Conselheiro Lopo Vaz 40, 1800-143 Lisboa, Portugal
4Instituto de Biología Molecular y Celular de Plantas, Consejo Superior de Investigaciones Científicas-UPV, Ingeniero Fausto Elio s/n, 46022 València, Spain
The theory of ecological stoichiometry considers ecological interactions among species with different chemical compositions. Both experimental and theoretical investigations have shown the importance of species composition in the outcome of the population dynamics. A recent study of a theoretical three-species food chain model considering stoichiometry [B. Deng and I. Loladze, Chaos 17, 033108 (2007)] shows that coexistence between two consumers predating on the same prey is possible via chaos. In this work we study the topological and dynamical measures of the chaotic attractors found in such a model under ecological relevant parameters. By using the theory of symbolic dynamics, we first compute the topological entropy associated with unimodal Poincaré return maps obtained by Deng and Loladze from a dimension reduction. With this measure we numerically prove chaotic competitive coexistence, which is characterized by positive topological entropy and positive Lyapunov exponents, achieved when the first predator reduces its maximum growth rate, as happens at increasing delta1. However, for higher values of delta1 the dynamics become again stable due to an asymmetric bubble-like bifurcation scenario. We also show that a decrease in the efficiency of the predator sensitive to prey's quality (increasing parameter zeta) stabilizes the dynamics. Finally, we estimate the fractal dimension of the chaotic attractors for the stoichiometric ecological model. ©2010 American Institute of Physics
History: Received 30 November 2009; accepted 24 June 2010; published 23 July 2010
Permalink: http://link.aip.org/link/?CHAOEH/20/033105/1

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