%0 Journal Article %1 baurmann2007instabilities %A Baurmann, M %A Gross, T %A Feudel, U %D 2007 %J J Theor Biol %K Turing_bifurcation predator-prey spatial_structure %N 2 %P 220-229 %R 10.1016/j.jtbi.2006.09.036 %T Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations %U http://www.ncbi.nlm.nih.gov/pubmed/17140604 %V 245 %X 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.

@article{baurmann2007instabilities, 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.}, added-at = {2014-12-05T02:03:53.000+0100}, author = {Baurmann, M and Gross, T and Feudel, U}, biburl = {https://www.bibsonomy.org/bibtex/2f63eb9f81140e493f0e30c3b30008b81/peter.ralph}, doi = {10.1016/j.jtbi.2006.09.036}, interhash = {a2b90559b54bf542083a959006c81078}, intrahash = {f63eb9f81140e493f0e30c3b30008b81}, journal = {J Theor Biol}, keywords = {Turing_bifurcation predator-prey spatial_structure}, month = mar, number = 2, pages = {220-229}, pmid = {17140604}, timestamp = {2014-12-05T02:03:53.000+0100}, title = {Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations}, url = {http://www.ncbi.nlm.nih.gov/pubmed/17140604}, volume = 245, year = 2007 }