# Self-similar Turing patterns: An anomalous diffusion consequence.

@article{Hernndez2017SelfsimilarTP, title={Self-similar Turing patterns: An anomalous diffusion consequence.}, author={D. Hern{\'a}ndez and Erik C{\'e}sar Herrera-Hern{\'a}ndez and Mayra N{\'u}{\~n}ez-L{\'o}pez and H. Hernandez-Coronado}, journal={Physical review. E}, year={2017}, volume={95 2-1}, pages={ 022210 } }

In this work, we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through diffusion-driven instability. We also find spiral patterns and patterns with mixtures of rotational symmetries. The type of anomalous diffusion discussed in this work, either subdiffusion or superdiffusion, is a consequence of the medium heterogeneity, and it is modeled through a space-dependent diffusion coefficient with a power-law…

## Figures and Topics from this paper

## 8 Citations

Turing instability conditions in confined systems with an effective position-dependent diffusion coefficient.

- Medicine, PhysicsThe Journal of chemical physics
- 2020

It is found that under this approximation, Turing instability conditions can be modified due to the channel geometry, and the dispersion relation, range of unstable modes where pattern formation occurs, and spatial structure of the patterns itself change as functions of the geometric parameters of the channel.

Analytic approaches of the anomalous diffusion: A review

- PhysicsChaos, Solitons & Fractals
- 2019

Abstract This review article aims to stress and reunite some of the analytic formalism of the anomalous diffusive processes that have succeeded in their description. Also, it has the objective to…

Decaying localized structures beyond Turing space in an activator–inhibitor system

- Physics
- 2020

We perform numerical simulations beyond Turing space in an activator–inhibitor system involving quadratic and cubic nonlinearities . We show that while all the three fixed points of the system are…

Bifurcation and patterns induced by flow in a prey-predator system with Beddington-DeAngelis functional response.

- Physics, MedicinePhysical review. E
- 2020

Numerical bifurcation analyses are consistent with the analytical results and show that the patterns induced by flow may be traveling waves with different wavelengths, amplitudes, and speeds, which are illustrated by numerical simulations.

Validation of numerical solution of diffusive part in a reaction-diffusion model

- Mathematics, Computer ScienceComput. Math. Appl.
- 2017

A methodological procedure to validate the numerical solution of the diffusive part in a reaction–diffusion model using Uniform explicit finite differences method to generate the solution in a confined circular domain with boundary condition of zero flux.

Spot Dynamics in a Reaction-Diffusion Model of Plant Root Hair Initiation

- Biology, PhysicsSIAM J. Appl. Math.
- 2018

We study pattern formation in a 2-D reaction-diffusion (RD) sub-cellular model characterizing the effect of a spatial gradient of a plant hormone distribution on a family of G-proteins associated…

Spot dynamics in a reaction-diffusion model of plant root hair initiation

- Biology, Physics
- 2017

We study pattern formation aspects in a 2-D reaction-diffusion (RD) sub-cellular model characterizing the effect of a spatial gradient of a plant hormone distribution on a family of G-proteins…

On the effective diffusion in the Sierpiński carpet

- MathematicsComputational Geosciences
- 2020

In this work, we use the method of volume averaging to upscale the pore-scale diffusion equation on the Sierpiński carpet. Based on the isotropy condition in the fractal structure and the fact that…

## References

SHOWING 1-10 OF 19 REFERENCES

Reaction-Transport Systems: Mesoscopic Foundations, Fronts, and Spatial Instabilities

- Mathematics
- 2010

General Concepts.- Reaction Kinetics.- Reactions and Transport: Diffusion, Inertia, and Subdiffusion.- Random Walks and Mesoscopic Reaction-Transport Equations.- Front Propagation.-…

Phys

- Rev. E 65, 051913
- 2002

Phys

- Chem. Chem. Phys, 16
- 2014

Phys

- Rev. E 88, 063004
- 2013

Water Resour

- Res. 49, 7
- 2013

Phys

- Rev. E 85, 066316
- 2012

Phys

- Rev. E 79, 026109
- 2009

Phys

- Rev. E 74, 046116
- 2006

Journal of Physics A 37

- 2004