TY - JOUR
T1 - Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations
AU - Baurmann, Martin
AU - Gross, Thilo
AU - Feudel, Ulrike
PY - 2007
Y1 - 2007
N2 - 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.
AB - 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.
U2 - 10.1016/j.jtbi.2006.09.036
DO - 10.1016/j.jtbi.2006.09.036
M3 - Article (Academic Journal)
C2 - 17140604
VL - 245
SP - 220
EP - 229
JO - Journal of Theoretical Biology
JF - Journal of Theoretical Biology
SN - 0022-5193
IS - 2
ER -