Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations |
| |
Authors: | Baurmann Martin Gross Thilo Feudel Ulrike |
| |
Institution: | Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky University, 26111 Oldenburg, Germany. baurmann@icbm.de |
| |
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. |
| |
Keywords: | Predator-prey models Turing-Hopf bifurcation Turing-Takens-Bogdanov bifurcation Pattern formation |
本文献已被 ScienceDirect PubMed 等数据库收录! |