Corpus ID: 209461016

The impact of advection on large-wavelength stability of stripes near planar Turing instabilities

@article{Yang2019TheIO,
  title={The impact of advection on large-wavelength stability of stripes near planar Turing instabilities},
  author={Jichen Yang and J. Rademacher and E. Siero},
  journal={arXiv: Analysis of PDEs},
  year={2019}
}
It is well known that for reaction-diffusion systems with differential isotropic diffusions, a Turing instability yields striped solutions. In this paper we study the impact of weak anisotropy by directional advection on such solutions, and the role of quadratic terms. We focus on the generic form of planar reaction-diffusion systems with two components near such a bifurcation. Using Lyapunov-Schmidt reduction and Floquet-Bloch decomposition we derive a rigorous parameter expansion for… Expand

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References

SHOWING 1-10 OF 22 REFERENCES
Transverse instabilities in chemical Turing patterns of stripes.
TLDR
By means of the amplitude equation formalism, it is shown that, close to the hexagon-stripe transitions, these sideband instabilities may be preceded by an amplitude instability that grows transient spots locally before reconnecting with stripes. Expand
Striped pattern selection by advective reaction-diffusion systems: resilience of banded vegetation on slopes.
TLDR
It is numerically show that the resilience of the vegetation bands is larger on steeper slopes by computing the stability regions (Busse balloons) of striped patterns with respect to 1D and transverse 2D perturbations, and proves a "Squire theorem" for a class of two-component reaction-advection-diffusion systems that includes this model. Expand
The Dynamics of Modulated Wave Trains
The authors of this title investigate the dynamics of weakly-modulated nonlinear wave trains. For reaction-diffusion systems and for the complex Ginzburg - Landau equation, they establish rigorouslyExpand
Nonlinear dynamic and pattern bifurcations in a model for spatial patterns in young mussel beds
TLDR
It is shown that spatial patterns occur for a wide range of algal concentrations, even when algal concentration is much lower than the prediction by linear analysis in the RDA model, which is to say, spatial patterns result from the interaction of nonlinear terms. Expand
Nonlinear stability analyses of Turing patterns for a mussel-algae model
A particular interaction–diffusion mussel-algae model system for the development of spontaneous stationary young mussel bed patterning on a homogeneous substrate covered by a quiescent marine layerExpand
The development of spatial structure in an ionic chemical system induced by applied electric fields
The spatio-temporal structures that can arise in an ionic chemical system with a cubic autocatalytic reaction step (Gray-Scott kinetics) in the presence of an applied electric field are described. AExpand
Chapter 18 - Stability of Travelling Waves
Abstract An overview of various aspects related to the spectral and nonlinear stability of travelling-wave solutions to partial differential equations is given. The point and the essential spectrumExpand
A New Approach to Sideband-Instabilities Using the Principle of Reduced Instability
First we develop the theory of reduced instability in order to analyze stability of bifurcating solutions via the Liapunov{Schmidt reduction. Next, this theory is generalized to cover sidebandExpand
Chemical instability induced by a differential flow.
TLDR
A new kind of instability is predicted for a system involving activator and inhibitor kinetics in a reactive flow that is free from the restrictions of the Turing instability on the diffusion coefficients and can thus be expected to occur in a wide variety of natural and artificial systems. Expand
pde2path - A Matlab package for continuation and bifurcation in 2D elliptic systems
pde2path is a free and easy to use Matlab continuation/bifurcation package for elliptic systems of PDEs with arbitrary many components, on general two dimensional domains, and with rather generalExpand
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