Instability in Reaction-Superdiffusion Systems
Abstract
We study the effect of superdiffusion on the instability in reaction-diffusion systems. It is shown that reaction-superdiffusion systems close to a Turing instability are equivalent to a time-dependent Ginzburg-Landau model and the corresponding free energy is introduced. This generalized free energy which depends on the superdiffusion exponent governs the stability, dynamics and the fluctuations of reaction-superdiffusion systems near the Turing bifurcation. In addition, we show that for a general n-component reaction-superdiffusion system, a fractional complex Ginzburg- Landau equation emerges as the amplitude equation near a Hopf instability. Numerical simulations of this equation are carried out to illustrate the effect of superdiffusion on spatio-temporal patterns. Finally the effect of superdiffusion on the instability in Brusselator model, as a special case of reaction-diffusion systems, is studied. In general superdiffusion introduces a new parameter that changes the behavior of the system near the instability.
Cite
@article{arxiv.1611.07744,
title = {Instability in Reaction-Superdiffusion Systems},
author = {Reza Torabi and Zahra Rezaei},
journal= {arXiv preprint arXiv:1611.07744},
year = {2016}
}
Comments
28 pages, 5 figures