• Open Access

Forced patterns near a Turing-Hopf bifurcation

Chad M. Topaz and Anne J. Catllá
Phys. Rev. E 81, 026213 – Published 26 February 2010

Abstract

We study time-periodic forcing of spatially extended patterns near a Turing-Hopf bifurcation point. A symmetry-based normal form analysis yields several predictions, including that (i) weak forcing near the intrinsic Hopf frequency enhances or suppresses the Turing amplitude by an amount that scales quadratically with the forcing strength, and (ii) the strongest effect is seen for forcing that is detuned from the Hopf frequency. To apply our results to specific models, we perform a perturbation analysis on general two-component reaction-diffusion systems, which reveals whether the forcing suppresses or enhances the spatial pattern. For the suppressing case, our results are consistent with features of previous experiments on the chlorine dioxide-iodine-malonic acid chemical reaction. However, we also find examples of the enhancing case, which has not yet been observed in experiment. Numerical simulations verify the predicted dependence on the forcing parameters.

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  • Received 2 July 2009

DOI:https://doi.org/10.1103/PhysRevE.81.026213

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Authors & Affiliations

Chad M. Topaz

  • Department of Mathematics, Statistics, and Computer Science, Macalester College, St. Paul, Minnesota 55105, USA

Anne J. Catllá

  • Department of Mathematics, Wofford College, Spartanburg, South Carolina 29303, USA

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Issue

Vol. 81, Iss. 2 — February 2010

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