A family of stochastic processes has quasi-cycle oscillations if its otherwise-damped oscillations are sustained by noise. Such a family forms the reaction part of a stochastic reaction-diffusion system when we insert a local Mexican Hat-type, difference of Gaussians, coupling on a one-dimensional and on a two-dimensional lattice. We find spatial patterns of oscillating quasicycles that resembl...

actants is used to compute the time evolution of reactant concentrations. The stochastic algorithm is rigorous in the The stochastic time evolution method has been used previously to study non-linear chemical reaction processes in well-stirred hosense that it provides an exact solution to the correspondmogeneous systems. We present the first treatment of diffusion, in ing master equation for ch...

Abstract. A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge of stochastic simulations is assumed. The methods are explained using illustrative examples. The article starts with the classical Gillespie algorithm for the stochastic modelling of chemical reactions. Then stochastic algorithms for modelling molecular diffusion are given...

<p style='text-indent:20px;'>We consider the control of semilinear stochastic partial differential equations (SPDEs) via deterministic controls. In case multiplicative noise, existence optimal controls and necessary conditions for optimality are derived. additive we obtain a representation gradient cost functional adjoint calculus. The restriction to noise avoids necessity introducing bac...

Here we present a study of stochastic resonance in an extended FitzHugh-Nagumo system with a field dependent activator diffusion. We show that the system response (here measured through the output signal-to-noise ratio) is enhanced due to the particular form of the non-homogeneous coupling. Such a result supports previous ones obtained in a simpler scalar reaction-diffusion system and shows tha...

7 reaction-diffusion system at appropriate values of the rate coefficients and particles’ diffusion constant. This relationship is called “duality” by the probabilists; it is not via some hydrodynamic description of the interacting particle system. In this paper we present a complete derivation of the duality relationship and use it to deduce some properties of solutions to the stochastic Fishe...

We propose a new method for polarimetric synthetic aperture radar (PolSAR) imagery classification based on stochastic distances in the space of random matrices obeying complex Wishart distributions. Given a collection of prototypes [Formula: see text] and a stochastic distance d(.,.), we classify any random matrix X using two criteria in an iterative set-up. First, we associate X with the class...