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Solution of the master equation of a bistable reaction system

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  • Wissel, Christian

Abstract

In this paper several dynamical properties of the stochastic Schlögl model are calculated. A semi-numerical method of solving the eigenvalue problem of the corresponding master equation enables us to determine all interesting quantities to a very high accuracy. The dependence of the metastable state on the various parameters is shown. The transient evolution in a quenching process is investigated. It is shown how the deterministic discontinuous transition is altered by the stochastics. Finally, the dynamical correlation function has been determined in the bistability region. The demonstrated method can generally be used for the solution of a one-dimensional single step master equation.

Suggested Citation

  • Wissel, Christian, 1984. "Solution of the master equation of a bistable reaction system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(1), pages 150-163.
    • Handle: RePEc:eee:phsmap:v:128:y:1984:i:1:p:150-163
    DOI: 10.1016/0378-4371(84)90085-2
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    References listed on IDEAS

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    1. West, Bruce J. & Lindenberg, Katja & Seshadri, V., 1980. "Brownian motion of harmonic systems with fluctuating parameters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 102(3), pages 470-488.
    2. Ebeling, W. & Schimansky-Geier, L., 1979. "Stochastic dynamics of a bistable reaction system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 98(3), pages 587-600.
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