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

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

2012-04-19

arxiv.org/abs/1204.4464v1

Mathematics

Dynamical Systems

Scientific paper

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.

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