Regensburg 1998 – scientific programme

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DY: Dynamik und Statistische Physik

DY 46: POSTER II

DY 46.37: Poster

Thursday, March 26, 1998, 14:30–17:30, B

Weakly Non-Linear Analysis of Reaction-Diffusion Systems with Non-Local Coupling — •Ernesto Nicola and Markus Bär — Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden

Two variable reaction-diffusion systems with non-local coupling have richer behaviour than standard activator-inhibitor models. More specifically, the different form of spatial coupling introduces new pattern-forming instabilities. We apply the method of weakly non-linear analysis to these systems, obtaining amplitude equations that give a description of the dynamics of the system near the instability. To test this methods, we study systems that have wave instabilities (oscillatory bifurcation with nonzero wavenumber). We can identify regimes of traveling resp. standing waves from the amplitude equations and compare to the outcome of direct simulations. In the traveling wave case, coherent structures like sinks and sources are found. A detailed analysis of these structures is performed by comparing predictions from the amplitude equations with numerical results of the original model.