Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 541683, 12 pages
Research Article

Chaos in Ecology: The Topological Entropy of a Tritrophic Food Chain Model

Jorge Duarte,1,2 Cristina Januário,1 and Nuno Martins3

1Department of Chemistry, Mathematics Unit, ISEL-High Institute of Engineering of Lisbon, rua Conselheiro Emídio Navarro 1, 1959-007 Lisbon, Portugal
2Research Centre in Mathematics and Applications (CIMA), University of Evora, rua Romão Ramalho 59, 7000-671 Evora, Portugal
3Department 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, Portugal

Received 9 December 2007; Accepted 18 June 2008

Academic Editor: A. Reggiani

Copyright © 2008 Jorge Duarte et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.