Journal
JOURNAL OF THEORETICAL BIOLOGY
Volume 245, Issue 2, Pages 220-229Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jtbi.2006.09.036
Keywords
predator-prey models; Turing-Hopf bifurcation; Turing-Takens-Bogdanov bifurcation; pattern formation
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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. (c) 2006 Elsevier Ltd. All rights reserved.
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