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arXiv · 1204.4464

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

A. J. Roberts
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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.

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A. J. Roberts. 2012-04-19. Computer algebra compares the stochastic superslow manifold of an averaged SPDE with that of the original slow-fast SPDE. https://arxiv.org/abs/1204.4464

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