In this article, we obtain a central limit theorem and prove moderate deviation principle for stochastic reaction-diffusion systems with multiplicative noise non-Lipschitz reaction term.

Almost nothing decisive has been said about collocation methods for solving SPDEs. Among the best of such SPDEs the Burgers equation shows a prototypical model for describing the interaction between the reaction mechanism, convection effect, and diffusion transport. This paper discusses spectral collocation method to reduce stochastic Burgers equation to a system of stochastic ordinary differen...

In this article, we prove the existence of a random attractor of the stochastic three-component reversible Gray-Scott system on infinite lattice with additive noise. We use a transformation of addition involved with Ornstein-Uhlenbeck process, for proving the pullback absorbing property and the pullback asymptotic compactness of the reaction diffusion system with cubic nonlinearity.

Existence of global classical solutions of a class of reaction–diffusion systems with chemotactic terms is demonstrated. This class contains a system of equations derived recently as a continuous limit of the stochastic discrete cellular Potts model. This provides mathematical justification for using numerical solutions of this system for modeling cellular motion in a chemotactic field. © 2009 ...

Turing proposed a mathematical model based on chemical reactions and diffusion of substances throughout the xy-plane, called reaction-diffusion, to study the emergence of patterns from a homogeneous medium [65]. Hammel and Prusinkiewicz used L-systems and reaction-diffusion in a one-dimensional medium to model the formation of sea shell patterns, and in an expanding one-dimensional medium to mo...

Spatial stochastic simulation is a valuable method for studying processes of reaction and diffusion in biological systems. This technique requires significant computational efforts, but the availability of high-performance computing made it possible to develop coherent computational models of cells [1]. Several approaches were introduced in order to utilize parallel execution to speed up simula...