Computer algebra compares the stochastic superslow manifold of an averaged SPDE with that of the original slow-fast SPDE

TL;DR

This paper uses computer algebra to compare the superslow manifolds of averaged and original stochastic PDEs in a slow-fast system, validating the averaging in large deviation regimes.

Contribution

It introduces computer algebra routines to analyze and compare superslow manifolds of averaged and original SPDEs in slow-fast stochastic systems.

Findings

The superslow models of averaged and original systems are consistent in a stochastic bifurcation regime.

Computer algebra routines facilitate detailed analysis of slow-fast stochastic dynamics.

Validation of the averaging principle in the context of large deviations for SPDEs.

Abstract

The computer algebra routines documented here empower you to reproduce and check many of the details described by an article on large deviations for slow-fast stochastic systems [abs:1001.4826]. We consider a 'small' spatial domain with two coupled concentration fields, one governed by a 'slow' reaction-diffusion equation and one governed by a stochastic 'fast' linear equation. In the regime of a stochastic bifurcation, we derive two superslow models of the dynamics: the first is of the averaged model of the slow dynamics derived via large deviation principles; and the second is of the original fast-slow dynamics. Comparing the two superslow models validates the averaging in the large deviation principle in this parameter regime.