Chemical turbulence equivalent to Nikolavskii turbulence

Abstract

We find evidence that a certain class of reaction-diffusion systems can exhibit chemical turbulence equivalent to Nikolaevskii turbulence. The distinctive characteristic of this type of turbulence is that it results from the interaction of weakly stable long-wavelength modes and unstable short-wavelength modes. We indirectly study this class of reaction-diffusion systems by considering an extended complex Ginzburg-Landau (CGL) equation that was previously derived from this class of reaction-diffusion systems. First, we show numerically that the power spectrum of this CGL equation in a particular regime is qualitatively quite similar to that of the Nikolaevskii equation. Then, we demonstrate that the Nikolaevskii equation can in fact be obtained from this CGL equation through a phase reduction procedure applied in the neighborhood of a codimension-two Turing--Benjamin-Feir point.

10 pages, 3 figures

References in corpus (1)

• Rotating Spirals without Phase Singularity in Reaction-Diffusion Systems

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• Critical exponents of Nikolaevskii turbulence
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• Arnol'd Tongues in Oscillator Systems with Nonuniform Spatial Driving
• Self-sustained patchy turbulence in shear-thinning active fluids
• Bifurcation scenario to Nikolaevskii turbulence in small systems
• Coarsening to Chaos-Stabilized Fronts
• Application of the Kudryashov method for finding exact solutions of the high order nonlinear evolution equations