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Stochastic dynamics of a bistable reaction system

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  • Ebeling, W.
  • Schimansky-Geier, L.

Abstract

The method of stochastic dynamics is used for the study of a discrete trimolecular chemical model with internal fluctuations. Several trajectories of the phase point are simulated for the bistable Schlögl model at small volumes. The influence due to the discontinuity of the process on the stationary probability distribution function is analyzed. The transition to the bimodal distribution is shown to be a cusp catastrophe. The location of the cuspoid strongly depends on the reaction volume. Autocorrelation functions are calculated numerically for short and large time scales.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:98:y:1979:i:3:p:587-600
    DOI: 10.1016/0378-4371(79)90157-2
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    References listed on IDEAS

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    1. Feistel, R. & Ebeling, W., 1978. "Deterministic and stochastic theory of sustained oscillations in autocatalytic reaction systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 93(1), pages 114-137.
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    Cited by:

    1. Schweitzer, Frank & Schimansky-Geier, Lutz & Ebeling, Werner & Ulbricht, Heinz, 1988. "A stochastic approach to nucleation in finite systems: Theory and computer simulations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 150(1), pages 261-279.
    2. Frankowicz, M. & Gudowska-Nowak, E., 1982. "Stochastic simulation of a bistable chemical system: The two-box model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 116(1), pages 331-344.
    3. Frankowicz, M. & Turner, J.W., 1986. "The two-box model of a bistable chemical system: Stationary probability distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 135(2), pages 591-600.
    4. Ebeling, W. & Engel-Herbert, H., 1980. "The influence of external fluctuations on self-sustained temporal oscillations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 104(3), pages 378-396.
    5. 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.

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    1. Ebeling, W. & Engel-Herbert, H., 1980. "The influence of external fluctuations on self-sustained temporal oscillations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 104(3), pages 378-396.

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