Numerical integration of a stochastic model for the Volterra-Lotka reaction |
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Authors: | Janet Walker Anne Van Nypelseer W. E. Langlois |
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Affiliation: | 1. Mills College, 94613, Oakland, CA 2. Faculté des Sciences, Université Libre de Bruxelles, 1050, Bruxelles, Belgium 3. IBM Research Laboratory, 95193, San Jose, CA
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Abstract: | Time-integration of the master equation governing the birth-and-death model of the Volterra-Lotka reaction is carried out for three different initial conditions, with the results: - Fluctuations destroy the deterministic steady state in a manner quantitatively predicted from a cumulant expansion;
- The sustained oscillatory behavior predicted by the deterministic model degenerated after 1/4 cycle in the stochastic model;
- It is possible to select initial distributions such that the asymptotic distribution is a spike at the origin of the plane of reactants.
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