Stochastic reaction-diffusion equations

Active media are a suitable benchmark to study the constructive role of random fluctuations in pattern forming systems. The mathematical framework to model these pattern forming systems is by using Partial Differential Equations. The interaction between the non-linearities and the random perturbations can give rise to unexpected phenomena. Several types of non-linear systems are considered and in particular extended chemical reacions where the noise is externally controlled by a computer. White, globally temporal or spatio-temporal noises interact with spiral waves, Turing patterns, oscillations and traveling waves in a contra-intuitive way.

Related Publications

Noise-reversed stability of Turing patterns versus Hopf oscillations near codimension-two conditions.
S. Alonso and F. Sagués, Phys. Rev. E 80, 035203(R) (2009).

Effects of external global noise on the catalytic CO oxidation on Pt(110).
P. S. Bodega, S. Alonso and H. H. Rotermund. J. Chem. Phys. 130, 084704 (2009).

Differential susceptibity to noise of mixed Turing and Hopf modes in a photosensitive chemical medium.
S. Alonso, D. G. Míguez and F. Sagués, Europhys. Lett. 81, 30006 (2008).

Scroll Wave Instability Controlled by External Fluctuations.
F. Sagués, S. Alonso and J. M. Sancho. Physica A 351, 159 (2005).

Suppression of Scroll Wave Turbulence by Noise.
S. Alonso, J. M. Sancho and F. Sagués. Phys. Rev. E 70, 067201 (2004).

Wave Pattern Dynamics in Fluctuating media.
F. Sagués, S. Alonso and J. M. Sancho. Int. J. Mod. Phys. C 13, 1243 (2002).

Excitability Transitions and Wave Dynamics under Spatiotemporal Structured Noise.
S. Alonso, F. Sagués and J. M. Sancho. Phys. Rev. E 65, 066107 (2002).

Regular Wave Propagation out of Noise in Chemical Active Media.
S. Alonso, I. Sendiña-Nadal, V. Pérez-Muñuzuri, J. M. Sancho and F. Sagués. Phys. Rev.
Lett. 87, 078302 (2001).

Noise-induced Brownian Motion of Spiral Waves.
S. Alonso and F. Sagués. Phys. Rev. E 63, 046205 (2001).

Brownian Motion of Spiral Waves Driven by Spatiotemporal Structured Noise.
I. Sendiña-Nadal, S. Alonso, V. Pérez-Muñuzuri, M. Gómez-Gesteira, V. Pérez-Villar, J.
Casademunt, J. M. Sancho and F. Sagués. Phys. Rev. Lett. 84, 2734 (2000).