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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

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

Pages: 1775 - 1794, Volume 17, Issue 6, September 2012      doi:10.3934/dcdsb.2012.17.1775

 
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Parker Childs - Department of Mathematics, University of Utah, Salt Lake City, UT 84112, United States (email)
James P. Keener - Department of Mathematics, University of Utah, Salt Lake City, UT 84112, United States (email)

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.

Keywords:  Chemical master equations, slow manifold reduction, stochastic chemical reactions, Markov processes, autocatalytic reactions, spectral gap theory.
Mathematics Subject Classification:  Primary: 60J27, 34E13; Secondary: 80A30.

Received: May 2011;      Revised: November 2011;      Available Online: May 2012.

 References