- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 465183, 10 pages
Periodic Orbits for a Three-Dimensional Biological Differential Systems
1Departamento de Matemáticas, Pontificia Universidad Javeriana, Carrera 7, No. 43-82, Bogotá, Colombia
2Departamento de Ciencias Naturales y Matemáticas, Facultad de Ingeniería, Pontificia Universidad Javeriana, Cali, Colombia
Received 3 June 2013; Accepted 7 June 2013
Academic Editor: Luca Guerrini
Copyright © 2013 Renato Colucci and Daniel Nuñez. 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.
- B. Bolker, M. Holyoak, V. Křivan, L. Rowe, and O. Schmitz, “Connecting theoretical and empirical studies of trait-mediated interactions,” Ecology, vol. 84, no. 5, pp. 1101–1114, 2003.
- D. Cariveau, R. E. Irwin, A. K. Brody, L. S. Garcia-Mayeya, and A. Von Der Ohe, “Direct and indirect effects of pollinators and seed predators to selection on plant and floral traits,” Oikos, vol. 104, no. 1, pp. 15–26, 2004.
- B. A. Menge, “Indirect effects in marine rocky intertidal interaction webs: patterns and importance,” Ecological Monographs, vol. 65, no. 1, pp. 21–74, 1995.
- W. E. Snyder and A. R. Ives, “Generalist predators disrupt biological control by a specialist parasitoid,” Ecology, vol. 82, no. 3, pp. 705–716, 2001.
- J. T. Wootton, “Indirect effects, prey susceptibility, and habitat selection: impacts of birds on limpets and algae,” Ecology, vol. 73, no. 3, pp. 981–991, 1992.
- M. R. Walsh and D.N. Reznick, “Interactions between the direct and indirect effects of predators determine life history evolution in a killifish,” Proceedings of the National Academy of Sciences of the United States of America, vol. 105, no. 2, pp. 594–599.
- D. O. Hessen, T. Andersen, P. Brettum, and B. A. Faafeng, “Phytoplankton contribution to sestonic mass and elemental ratios in lakes: implications for zooplankton nutrition,” Limnology and Oceanography, vol. 48, no. 3, 2003.
- J. Estes, K. Crooks, and R. Holt, Ecological Role of Predators, vol. 4 of Enciclopedia of Biodiversity, Academic Press, 2001.
- V. Lundgren and E. Granéli, “Grazer-induced defense in Phaeocystis globosa (Prymnesiophyceae): influence of different nutrient conditions,” Limnology and Oceanography, vol. 55, no. 5, 2010.
- M. F. Carusela, F. R. Momo, and L. Romanelli, “Competition, predation and coexistence in a three trophic system,” Ecological Modelling, vol. 220, no. 19, pp. 2349–2352, 2009.
- Indirect effects affects ecosystem dynamics, 2011, http://www.ictp-saifr.org/.
- R. Margalef, “Life forms of Phytoplanktos as survival alternative in an unstable environment,” Oceanologica Acta, vol. 134, 1978.
- O. Sarnelle, “Daphnia as keystone predators: effects on phytoplankton diversity and grazing resistance,” Journal of Plankton Research, vol. 27, no. 12, pp. 1229–1238, 2005.
- R. Colucci, “Coexistence in a one-predator, two-prey system with indirect effects,” Journal of Applied Mathematics, vol. 2013, Article ID 625391, 13 pages, 2013.
- H. L. Smith and H. R. Thieme, Dynamical Systems and Population Persistence, American Mathematical Society, 2011.
- G. Butler, H. I. Freedman, and P. Waltman, “Uniformly persistent systems,” Proceedings of the American Mathematical Society, vol. 96, no. 3, pp. 425–430, 1986.
- S. M. Shahruz and D. A. Kalkin, “Limit cycle behavior in three- or higher-dimensional non-linear systems: the Lotka-Volterra example,” Journal of Sound and Vibration, vol. 246, no. 2, pp. 379–386, 2001.
- P. Van Den Driessche and M. L. Zeeman, “Three-dimensional competitive Lotka-Volterra systems with no periodic orbits,” SIAM Journal on Applied Mathematics, vol. 58, no. 1, pp. 227–234, 1998.
- Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, Springer, 1998.
- J. Hulsman and F. J. Weissing, “Biodiversity of plankton by species oscillations and chaos,” Nature, vol. 402, pp. 407–410, 1999.
- J.-M. Ginoux, B. Rossetto, and J.-L. Jamet, “Chaos in a three-dimensional Volterra-Gause model of predator-prey type,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 15, no. 4, pp. 1689–1708, 2005.
- A. Klebanoff and A. Hastings, “Chaos in one-predator, two-prey models: general results from bifurcation theory,” Mathematical Biosciences, vol. 122, no. 2, pp. 221–233, 1994.