Self-Similarity and Attraction in Stochastic Nonlinear Reaction-Diffusion Systems

Self-Similarity and Attraction in Stochastic Nonlinear Reaction-Diffusion Systems

Similarity solutions play an important role in many fields of science: we consider here similarity in stochastic dynamics. Important issues are not only the existence of stochastic similarity, but also whether a similarity solution is dynamically attractive, and if it is, to what particular solution does the system evolve. By recasting a class of stochastic PDEs in a form to which stochastic ce...

Discreteness-induced Stochastic Steady State in Reaction Diffusion Systems: Self-consistent Analysis and Stochastic Simulations

A self-consistent equation to derive a discreteness-induced stochastic steady state is presented for reactiondiffusion systems. For this formalism, we use the so-called Kuramoto length, a typical distance over which a molecule diffuses in its lifetime, as was originally introduced to determine if local fluctuations influence globally the whole system. We show that this Kuramoto length is also r...

Reaction-diffusion Systems and Nonlinear Waves

The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation...

Stochastic Simulation of Reaction-Diffusion Systems

Stochastic Simulation of Reaction-Diffusion Systems

Reactiondiffusion systems are mathematical models that describe how the concentration of one or more substances distributed in space changes under the influence of local chemical reactions in which the substances are converted into each other, and diffusion which causes the substances to spread out in space. The classical representation of a reaction-diffusion system is given by semi-linear par...