Instabilities in Spatially Extended Predator-prey Systems: Spatio-temporal Patterns in the Neighborhood of Turing-hopf Bifurcations.
From: Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky University, 26111 Oldenburg, Germany. baurmann@icbm.de
Journal of theoretical biology
- Publish Date: Mar 2007
- ISSN: 0022-5193
- Volume: 245
- Issue: 2
- Pages: 220-9
- Medium: Print
- Language: English
- Citation (JAMA): Baurmann Martin, Gross Thilo, Feudel Ulrike, et al. Instabilities in Spatially Extended Predator-prey Systems: Spatio-temporal Patterns in the Neighborhood of Turing-hopf Bifurcations.. J. Theor. Biol. Mar 2007;245:220-9
Abstract
We investigate the emergence of spatio-temporal patterns in ecological systems. In particular, we study a generalized predator-prey system on a spatial domain. On this domain diffusion is considered as the principal process of motion. We derive the conditions for Hopf and Turing instabilities without specifying the predator-prey functional responses and discuss their biological implications. Furthermore, we identify the codimension-2 Turing-Hopf bifurcation and the codimension-3 Turing-Takens-Bogdanov bifurcation. These bifurcations give rise to complex pattern formation processes in their neighborhood. Our theoretical findings are illustrated with a specific model. In simulations a large variety of different types of long-term behavior, including homogenous distributions, stationary spatial patterns and complex spatio-temporal patterns, are observed.
Mesh Headings (Keywords): Animals, Computer Simulation, Ecosystem, Feeding Behavior, Models, Psychological, Movement, Predatory Behavior
Check for Full Text / PubMed Unique Identifier (PMID): 17140604
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