Recent developments of fluorescence labeling and highly advanced microscopy techniques have enabled observations of activities of biosignaling molecules in living cells. The high spatial and temporal resolutions of these video microscopy experiments allow detection of fluorescence fluctuations at the timescales approaching those of enzymatic reactions. Such fluorescence fluctuation patterns may...

Reaction-diffusion systems are mathematical models that describe how the concentrations of substances distributed in space change under the influence of local chemical reactions, and diffusion which causes the substances to spread out in space. The classical representation of a reaction-diffusion system is given by semi-linear parabolic partial differential equations, whose solution predicts ho...

In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit original system is obtained, where an extra Gaussian term appears. Such explicitly given in terms of solution Poisson Hilbert space. Moreover, also obtain rate convergence, and convergence shown not to depend on regularity coeffic...

We have the purpose of analyzing the effect of explicit diffusion processes in a predator-prey stochastic lattice model. More precisely we wish to investigate the possible effects due to diffusion upon the thresholds of coexistence of species, i. e., the possible changes in the transition between the active state and the absorbing state devoid of predators. To accomplish this task we have perfo...

In this paper a stochastic reaction diffusion system is considered, which models the spread of a finite population reacting with a non-renewable resource in the presence of individual based noise. A two-parameter phase diagram is established to describe the large time evolution, distinguishing between certain death or possible life of the population.

The currently existing theory of fluorescence correlation spectroscopy (FCS) is based on the linear fluctuation theory originally developed by Einstein, Onsager, Lax, and others as a phenomenological approach to equilibrium fluctuations in bulk solutions. For mesoscopic reaction-diffusion systems with nonlinear chemical reactions among a small number of molecules, a situation often encountered ...

We investigate the critical behavior of a reaction-diffusion system exhibiting a continuous absorbing-state phase transition. The reaction-diffusion system strictly conserves the total density of particles, represented as a nondiffusive conserved field, and allows an infinite number of absorbing configurations. Numerical results show that it belongs to a wide universality class that also includ...

in this paper, we propose a new method for solving the stochastic advection-diffusion equation of ito type. in this work, we use a compact finite difference approximation for discretizing spatial derivatives of the mentioned equation and semi-implicit milstein scheme for the resulting linear stochastic system of differential equation. the main purpose of this paper is the stability investigatio...

In this report, we analyse and simulate a chemotaxis model given by a system of stochastic reaction-diffusion equations posed on an evolving surface.