Baurmann Martin, Gross Thilo, Feudel Ulrike
Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky University, 26111 Oldenburg, Germany.
J Theor Biol. 2007 Mar 21;245(2):220-9. doi: 10.1016/j.jtbi.2006.09.036. Epub 2006 Oct 14.
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.
我们研究生态系统中时空模式的出现。特别地，我们研究空间域上的广义捕食者 - 猎物系统。在这个域上，扩散被视为主要的运动过程。我们在不指定捕食者 - 猎物功能反应的情况下推导霍普夫（Hopf）和图灵（Turing）不稳定性的条件，并讨论它们的生物学意义。此外，我们识别余维数为 2 的图灵 - 霍普夫分岔和余维数为 3 的图灵 - 塔肯斯 - 博格达诺夫（Turing - Takens - Bogdanov）分岔。这些分岔在其邻域引发复杂的模式形成过程。我们的理论发现通过一个具体模型进行说明。在模拟中，观察到了各种各样不同类型的长期行为，包括均匀分布、静态空间模式和复杂的时空模式。
