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The influence of external fluctuations on self-sustained temporal oscillations

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  • Ebeling, W.
  • Engel-Herbert, H.

Abstract

The influence of external fluctuations on the bifurcational behavior of two-dimensional dynamical systems exhibiting limit cycles is investigated. Studying both exactly and approximately solvable examples it is shown that the variances of the external fluctuations occur as additional bifurcation parameters. The threshold values for soft as well as for hard self-excitation of oscillations are affected by the external fluctuations. To classify bifurcations of dynamical systems in the presence of fluctuations some aspects of catastrophe theory are applied to the corresponding stationary probability distributions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:104:y:1980:i:3:p:378-396
    DOI: 10.1016/0378-4371(80)90002-3
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    References listed on IDEAS

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    1. 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.
    2. 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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