Quasi-Patterns in a Model of Multi-Resonantly Forced Chemical Oscillations

Jessica Conway; Hermann Riecke

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arXiv · nlin/0703059

Quasi-Patterns in a Model of Multi-Resonantly Forced Chemical Oscillations

Jessica Conway·Hermann Riecke

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Abstract

Multi-frequency forcing of systems undergoing a Hopf bifurcation to spatially homogeneous oscillations is investigated using a complex Ginzburg-Landau equation that systematically captures weak forcing functions that simultaneously hit the 1:1-, the 1:2-, and the 1:3-resonance. Weakly nonlinear analysis shows that generically the forcing function can be tuned such that resonant triad interactions with weakly damped modes stabilize subharmonic quasipatterns with 4-fold and 5-fold rotational symmetry. In simulations starting from random initial conditions domains of these quasi-patterns compete and yield complex, slowly ordering patterns.

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Jessica Conway, Hermann Riecke. 2007-03-28. Quasi-Patterns in a Model of Multi-Resonantly Forced Chemical Oscillations. https://arxiv.org/abs/nlin/0703059

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