Incollection,
Stochastic resonance between patterns in anomalous diffusion--reaction systems: is normal diffusion a stochastic-resonant condition?
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
The usefulness of the nonequilibrium potential (NEP) framework for the study of stochastic resonance (SR) in reaction--diffusion systems has been highlighted by recent work for a review, see arXiv:. Not only does it provide a natural and general explanation to the phenomenon of system-size stochastic resonance (SSSR) Phys.\ Rev.\ E 72, 021101 (2005) but it allows to study the effects of e.g.\ selective coupling Phys.\ Rev.\ Lett.\ 84, 404 (2000); Physica A 374, 46 (2007) or nonlocal interactions, and even transcend the bistable regime towards the excitable one in activator--inhibitor systems.
Regarding nonlocal interactions, they may arise for several causes. A possible scenario is through the adiabatic elimination of a fast inhibitor in an activator-inhibitor system Phys.\ Rev.\ E 57, 5112 (1998); Phys.\ Rev.\ E 59, 5142 (1999); Physica A 376, 199 (2007). Another one is through an anomalous transport mechanism, relevant to pattern formation in nonhomogeneous media. Here we investigate that possibility by resorting to the fractional diffusion formalism. The form of the NEP is found here for such a situation, and exploited to analyze SR between patterns in an anomalous diffusion--reaction system. The exponent $\alpha$ of the fractional derivative plays a role analogous to that of the system's size in SSSR, so leaving room to speculation on the stochastic-resonant character of normal diffusion.
Tags
- anomalous
- diffusion
- formation
- nonequilibrium
- pattern
- potential
- reaction--diffusion
- resonance
- statphys23
- stochastic
- topic-3
