Studying partially ordered systems using stochastic differential equations by Rolls, E

“…<p>This thesis looks at two different problems in the field of partially ordered systems - modelling biopolymers on multiple scales as well as modelling two-dimensional nematic liquid crystal wells - and seeks to gain insight using stochastic differential equations, through mathematical analysis and numerical simulations. …”

A Constrained Approach to Multiscale Stochastic Simulation of Chemically Reacting Systems by Cotter, S, Zygalakis, K, Kevrekidis, I, Erban, R

“…We then show how using the ensuing Stochastic Differential Equation (SDE) approximation, we can in turn approximate average switching times in stochastic chemical systems.…”

Coarse-graining molecular dynamics: stochastic models with non-Gaussian force distributions by Erban, R

“…A family of stochastic coarse-grained (SCG) models, written as relatively low-dimensional systems of nonlinear stochastic differential equations, is presented. The nonlinear SCG model incorporates the non-Gaussian force distribution which is observed in MD simulations and which cannot be described by linear models. …”

On Cucker-Smale model with noise and delay by Erban, R, Haskovec, J, Sun, Y

“…The model is formulated as a system of delayed stochastic differential equations. It incorporates two additional processes which are present in animal decision making, but are often neglected in modelling: (i) stochasticity (imperfections) of individual behaviour; and (ii) delayed responses of individuals to signals in their environment. …”

Higher-order numerical methods for stochastic simulation of chemical reaction systems by Székely Jr., T, Burrage, K, Erban, R, Zygalakis, K

“…This approach, as in the case of ordinary and stochastic differential equations, can be repeated to obtain even higher-order approximations. …”

A higher-order numerical framework for stochastic simulation of chemical reaction systems. by Székely, T, Burrage, K, Erban, R, Zygalakis, K

“…As in the case of ordinary and stochastic differential equations, extrapolation can be repeated to obtain even higher-order approximations. …”

A higher-order numerical framework for stochastic simulation of chemical reaction systems by Szekely, T, Burrage, K, Erban, R, Zygalakis, K

“…As in the case of ordinary and stochastic differential equations, extrapolation can be repeated to obtain even higher-order approximations.…”