Regensburg 2004 – scientific programme

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AKB: Biologische Physik

AKB 50: Poster Session "Biological Physics"

AKB 50.115: Poster

Friday, March 12, 2004, 10:30–13:00, B

Hopf-bifurcations in systems with conserved quantities — •Markus Hilt and Walter Zimmermann — Theoretische Physik, Universität des Saarlandes, 66041 Saarbrücken

A cubic Ginzburg–Landau equation is presented, which describes for the first time the universal properties of a Hopf-bifurcation in a system with conserved quantities. This bifurcation occurs for instance in a model describing the dynamics of two interacting ion-channels in a membrane. It is a universal feature of this bifurcation that all nonlinear traveling wave solutions are linear unstable in general, besides the smallest possible wavenumber in a finite system with periodic boundary conditions. Spatio-temporal chaos occurs either due to boundary effects or due to an extension of the destabilizing wavenumber band. This scenario is different from other cases, where spatio-temporal chaos often occurs, as for instance for one of the most studied nonlinear equations in physics, the Ginzburg–Landau equation for unconserved systems (see e.g. I. Aranson and L. Kramer, Rev. Mod. Phys. 74, 99 (2002)).