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DY: Fachverband Dynamik und Statistische Physik

DY 17: Poster I

DY 17.27: Poster

Dienstag, 26. Februar 2008, 16:00–18:00, Poster C

Stationary Turing Patterns in the Diffusive Bazykin System — •Oliver Strebel — Handjerystr. 31 12159 Berlin

Recently McGehee et. al. [1] demonstrated the existence of Turing patterns in the diffusive Bazykin System within the framework of linear stabilty analysis. Time series from numerical integration of the parabolic Bazykin system underpinned this finding. In this study stationary Turing patterns of the time-independent elliptic Bazykin systemare calculated using fixed point methods.

The stability of various spatial modes is determined in the linear approximation. The stable modes emanating from the constant solution are continuated using numerical continuation methods [2]. They exhibit in course of the continuation gradually more anharmonic bahaviour. Numerical criteria for detecting tangent, pitchfork and Hopf bifurcations are employed [3]. These bifurcation points in turn are continuated numerically, giving a description of the systems behaviour in the parameter space.

[1] E. A. McGehee et al., Phys. Lett. A342 90 (2005) [2] E. L. Allgower and K. Georg, Numerical Continuation Methods, Springer (1990). [3] Yu. A. Kuznetsov, Elements of Applied Bifurcation Theory (3rd ed.), Springer AMS (2004).