Resonant suppression of Turing patterns by periodic illumination.

Abstract

We study the resonant behavior of Turing pattern suppression in a model of the chlorine dioxide-iodine-malonic acid reaction with periodic illumination. The results of simulations based on integration of partial differential equations display resonance at the frequency of autonomous oscillations in the corresponding well stirred system. The resonance in Turing pattern suppression is sharper at lower complexing agent concentration and is affected by the waveform of the periodic driving force. Square wave (on-off) periodic forcing is more effective in suppressing Turing patterns than sinusoidal forcing. We compare the dynamics of periodically forced Turing patterns with the dynamics of periodically forced nonhomogeneous states in a system of two identical coupled cells. Bifurcation analysis based on numerical continuation of the latter system gives good predictions for the boundaries of the major resonance regions of the periodically forced patterns.