Slow manifold reduction of a stochastic chemical reaction: Exploring Keizer's paradox

Parker Childs; James P. Keener

doi:10.3934/dcdsb.2012.17.1775

Article Contents

2012, Volume 17, Issue 6: 1775-1794. Doi: 10.3934/dcdsb.2012.17.1775

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Slow manifold reduction of a stochastic chemical reaction: Exploring Keizer's paradox

Parker Childs^1, and
James P. Keener^1,

1.
Department of Mathematics, University of Utah, Salt Lake City, UT 84112

Received: May 2011

Revised: November 2011

Published: September 2012

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Abstract

Keizer's paradox refers to the observation that deterministic and stochastic descriptions of chemical reactions can predict vastly different long term outcomes. In this paper, we use slow manifold analysis to help resolve this paradox for four variants of a simple autocatalytic reaction. We also provide rigorous estimates of the spectral gap of important linear operators, which establishes parameter ranges in which the slow manifold analysis is appropriate.

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Mathematics Subject Classification: Primary: 60J27, 34E13; Secondary: 80A30.

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