Stochastic dynamics on slow manifolds (Q2843739)

This work focuses on the study of stochastic dynamical systems and in particular on reduced descriptions of them. It proposes an extension of the slow manifold approach to the stochastic setting and both explains the general method and illustrates it with two particular examples. One of the highlights of the method is its applicability to stochastic differential equations that describe at the mesoscopic level individual based models. Individual based models are represented at the microscopic level by continuous-time Markov chains, and its appearance is frequent in the modeling of complex systems. The approximation consists in considering the full stochastic dynamics restricted to the slowest degrees of freedom of the deterministic system, giving rise this way to a lower-dimensional stochastic dynamical system that effectively describes the original one. This approximation is shown to match well with direct numerical simulations of the individual based models.