The nonlocal Fisher equation is a diffusion-reaction equation where the reaction has a linear birth term and a nonlocal quadratic competition, which describes the reaction between distant individuals. This equation arises in evolutionary biological systems, where the arena for the dynamics is trait space, diffusion accounts for mutations and individuals with similar traits compete, resulting in...

SUMMARY MesoRD is a tool for simulating stochastic reaction-diffusion systems as modeled by the reaction diffusion master equation. The simulated systems are defined in the Systems Biology Markup Language with additions to define compartment geometries. MesoRD 1.0 supports scale-dependent reaction rate constants and reactions between reactants in neighbouring subvolumes. These new features make...

To understand the chirality selection in the biological organic system, a simple lattice model of chemical reaction with molecular diffusion is proposed and studied by Monte Carlo simulations. In addition to a simple stochastic process of conversions between an achiral reactant A and chiral products, R and S molecules, a nonlinear autocatalysis is incorporated by enhancing the reaction rate fro...

Abstract We establish the existence of solutions to a class nonlinear stochastic differential equations reaction–diffusion type in an infinite-dimensional space, with diffusion corresponding given transition kernel. The solution obtained is scaling limit sequence interacting particle systems and satisfies martingale problem target equation.

We establish a convergence theorem for class of two components nonlinear reaction–diffusion systems. Each diffusion term is the subdifferential convex functional calculus variations whose equipped with Mosco-convergence. The reaction terms are structured in such way that systems admit bounded solutions, which positive modeling ecosystems. As consequence, under stochastic homogenization framewor...

In this paper, we present a novel method to estimate chemical reaction and diffusion rates for biochemical reaction–diffusion dynamics from time series of observations. Our approach leverages iterated particle filtering as means fit high-dimensional stochastic discrete spatiotemporal model sparse data, often with some species in low copy numbers. We demonstrate the feasibility on three realisti...

The paper is devoted to constructing a random exponential attractor for some classes of stochastic PDE’s. We first prove the existence of an exponential attractor for abstract random dynamical systems and study its dependence on a parameter and then apply these results to a nonlinear reaction-diffusion system with a random perturbation. We show, in particular, that the attractors can be constru...

We consider general singular control problems for random fields given by a stochastic partial differential equation (SPDE). We show that under some conditions the optimal singular control can be identified with the solution of a coupled system of SPDE and a reflected backward SPDE (RBSPDE). As an illustration we apply the result to a singular optimal harvesting problem from a population whose d...

Fluctuations in diffusion-controlled reactions lack the necessary features for a mesoscopic description. We show how the correlations dominate the dynamics by juxtaposing the macroscopic dynamics of a cellular automaton model for the diffusion-controlled limit to the deterministic diffusion-reaction rate equation for the same reaction. A more detailed N-body master equation is then presented in...

A class of Brownian dynamics algorithms for stochastic reaction-diffusion models which include reversible bimolecular reactions is presented and analyzed. The method is a generalization of the λ–̺ model for irreversible bimolecular reactions which was introduced in [11]. The formulae relating the experimentally measurable quantities (reaction rate constants and diffusion constants) with the algo...