Hamburg 2001 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 46: Poster
DY 46.21: Poster
Donnerstag, 29. März 2001, 15:45–18:15, Foyer S\ 3
Competing spatial and temporal instabilities in reaction-diffusion systems with subcritical spatial bifurcation — •E. Schöll1, S. Bose1, and P. Rodin2 — 1Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin — 2Ioffe Institute, St.Petersburg
The appearance of complex spatio-temporal behavior near a codimension-two bifurcation point is discussed for a class of reaction-diffusion systems exhibiting a subcritical spatial bifurcation followed by the formation of large-amplitude spatial patterns. Well developed techniques based on expansions near the uniform reference state (e.g., amplitude equations) fail in this case, and alternative approaches are required. We demonstrate that insight into the dynamics can be achieved by linearization in the vicinity of both the large-amplitude spatial pattern and the uniform reference state. A globally coupled reaction-diffusion model is taken as an example to illustrate this approach. We derive a sufficient criterion for the appearance of mixed spatio-temporal modes, and clarify the origin of a menagery of complex dynamics, such as periodic and chaotic oscillations of spatial patterns, low dimensional chaos including a Shil’nikov attractor, and periodic back-and-forth front motion. Special attention is devoted to the difference between spatio-temporal dynamics on one-dimensional and two-dimensional domains.