Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations.
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.
Baurmann
Martin
M
Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky University, 26111 Oldenburg, Germany. baurmann@icbm.de <baurmann@icbm.de>
Gross
Thilo
T
Feudel
Ulrike
U
D000818:Animals; D003198:Computer Simulation; D017753:Ecosystem; D005247:Feeding Behavior; D008960:Models, Psychological; D009068:Movement; D011235:Predatory Behavior