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Fluctuations in nonlinear systems near bifurcations corresponding to the appearance of new stable states

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  • Dykman, M.I.
  • Krivoglaz, M.A.

Abstract

Fluctuations in nonlinear multidimensional dynamical systems caused by outer δ-correlated random forces are considered. The slowness of one of the motions at parameter values within the bifurcation region allows us to use the adiabatic approximation and hence to reduce the multidimensional problem to a one-dimensional problem. The exponent and the pre-exponential factor in the expression for the probability of the transition from the metastable equilibrium state of the system are calculated. The kinetics of fluctuations in the systems that are near the bifurcation point where two stable states coincide is considered. The results are illustrated with an example of the Duffing nonlinear oscillator in an external resonance field.

Suggested Citation

  • Dykman, M.I. & Krivoglaz, M.A., 1980. "Fluctuations in nonlinear systems near bifurcations corresponding to the appearance of new stable states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 104(3), pages 480-494.
    • Handle: RePEc:eee:phsmap:v:104:y:1980:i:3:p:480-494
    DOI: 10.1016/0378-4371(80)90010-2
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    References listed on IDEAS

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    1. Tomita, Kazuhisa & Todani, Takao & Kidachi, Hideyuki, 1976. "Irreversible circulation and the undamped spiking in lasers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 84(2), pages 350-370.
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    Cited by:

    1. Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," EERI Research Paper Series EERI_RP_2003_04, Economics and Econometrics Research Institute (EERI), Brussels.
    2. Qi-Ming Chen & Michael Fischer & Yuki Nojiri & Michael Renger & Edwar Xie & Matti Partanen & Stefan Pogorzalek & Kirill G. Fedorov & Achim Marx & Frank Deppe & Rudolf Gross, 2023. "Quantum behavior of the Duffing oscillator at the dissipative phase transition," Nature Communications, Nature, vol. 14(1), pages 1-7, December.

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