Advertisement

Active Systems with Noise

  • Alexander S. Mikhailov
  • Alexander Yu. Loskutov
Part of the Springer Series in Synergetics book series (SSSYN, volume 52)

Abstract

The application of external noise causes a dynamical system to wander in its phase space. Such random wandering is superimposed on the steady drift produced by the deterministic dynamics. The resulting process is similar to the Brownian motion of a particle in the presence of a permanent driving force.

Keywords

Stochastic Differential Equation Multiplicative Noise Random Force Internal Noise Gaussian Random Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 9.1
    G.E. Uhlenbeck, L.S. Ornstein: Phys. Rev. 36, 823 (1930)ADSCrossRefGoogle Scholar
  2. 9.2
    S. Chandrasekhar: Rev. Mod. Phys. 15, 1 (1943)MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. 9.3
    T. Hida: Brownian Motion (Springer, Berlin, Heidelberg 1980)zbMATHGoogle Scholar
  4. 9.4
    R.L. Stratonovich: Topics in the Theory of Random Noise, Vols. I and II (Gordon and Breach, New York 1963 and 1967)Google Scholar
  5. 9.5
    L. Arnold: Stochastic Differential Equations: Theory and Applications (Wiley, New York 1974)zbMATHGoogle Scholar
  6. 9.6
    Z. Schuss: Theory and Applications of Stochastic Differential Equations (Wiley, New York 1980)zbMATHGoogle Scholar
  7. 9.7
    N.G. van Kampen: Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam 1983)Google Scholar
  8. 9.8
    C.W. Gardiner: Handbook of Stochastic Methods (Springer, Berlin, Heidelberg 1985)Google Scholar
  9. 9.9
    M. San Miguel, J.M. Sancho: “Langevin equations with coloured noise”, in Noise in Nonlinear Dynamical Systems; Theory, Experiment, Simulations, Vol. 1, ed. by F. Moss, P.V.E. McClintock (Cambridge University Press, Cambridge 1989) pp. 110–160Google Scholar
  10. 9.10
    R.L. Stratonovich: SIAM J. Control 4, 362 (1966)MathSciNetCrossRefGoogle Scholar
  11. 9.11
    K. Ito: Nagoya Math. J. 1, 35 (1950)MathSciNetzbMATHGoogle Scholar
  12. 9.12
    E. Wong, M. Zakai: Ann. Math. Stat. 36, 1560 (1965)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 9.13
    W. Horsthemke, R.L. Lefever: Noise-Induced Transitions (Springer, Berlin, Heidelberg 1984)zbMATHGoogle Scholar
  14. 9.14
    O.A. Druzhinin, A.S. Mikhailov: Izv. VUZ. Radiofizika 32, 444–450 (1989)Google Scholar
  15. 9.15
    M. Doi: J. Phys. A 9, 1465–1477 (1976)ADSCrossRefGoogle Scholar
  16. 9.16
    Ya.B. Zeldovich, A.A. Ochinnikov: Sov. Phys. JETP 47, 829 (1978)ADSGoogle Scholar
  17. 9.17
    A.S. Mikhailov: Phys. Lett. A 85, 214 (1981); A 85, 427 (1981)MathSciNetADSCrossRefGoogle Scholar
  18. 9.18
    A.M. Gutin, A.S. Mikhailov, V.V. Yashin: Sov. Phys. JETP 65, 535 (1987)Google Scholar
  19. 9.19
    A.S. Mikhailov: Phys. Rep. 184, 308–374 (1989)ADSCrossRefGoogle Scholar
  20. 9.20
    R. Landauer: “Noise-activated escape from metastable states: A historical review”, in Noise in Nonlinear Dynamical Systems; Theory, Experiment, Simulations, Vol. 1, ed. by F. Moss, P.V.E. McClintock (Cambridge University Press, Cambridge 1989) pp. 1–15Google Scholar
  21. 9.21
    P. Hanggi: J. Stat. Phys. 42, 105–148 (1986)MathSciNetADSCrossRefGoogle Scholar
  22. 9.22
    P.S. Martin, E.D. Siggia, H.A. Rose: Phys. Rev. A 8, 423 (1973)ADSCrossRefGoogle Scholar
  23. 9.23
    R. Graham: In Lecture Notes in Physics, Vol. 84 (Springer, Berlin, Heidelberg 1978) p. 82Google Scholar
  24. 9.24
    H.K. Janssen: Z. Phys. B 23, 377 (1976)ADSCrossRefGoogle Scholar
  25. 9.25
    R. Phytian: J. Phys. A 10, 777 (1977)MathSciNetADSCrossRefGoogle Scholar
  26. 9.26
    P. Hänggi: “Noise in continuous dynamical systems: A functional calculus approach”, in Noise in Nonlinear Dynamical Systems; Theory, Experiment, Simulations, Vol. 1, ed. by F. Moss, P.V.E. McClintock (Cambridge University Press, Cambridge 1989) pp. 307–328Google Scholar
  27. 9.27
    L. Pesquera, H.A. Rodrigues, E. Santos: Phys. Lett. A 94, 287 (1983)MathSciNetADSCrossRefGoogle Scholar
  28. 9.28
    A. Förster, A.S. Mikhailov: “Application of path integrals to stochastic reaction-diffusion equations”, in Selforganization by Nonlinear Irreversible Processes, ed. by W. Ebeling, H. Ulbricht (Springer, Berlin, Heidelberg 1986) pp. 89–94CrossRefGoogle Scholar
  29. 9.29
    H. Haken: Z. Phys. B 24, 321 (1976)MathSciNetADSCrossRefGoogle Scholar
  30. 9.30
    C. Wissel: Z.Phys. B 35, 185 (1979)MathSciNetADSCrossRefGoogle Scholar
  31. 9.31
    F. Langouche, D. Roekaerts, E. Tirapequi: Physica A 95, 252 (1979)MathSciNetADSCrossRefGoogle Scholar
  32. 9.32
    F. Langouche, D. Roekaerts, E. Tirapequi: Phys. Rev. D 20, 419 (1979); D 20, 433 (1979)MathSciNetADSCrossRefGoogle Scholar
  33. 9.33
    A. Förster, A.S. Mikhailov: Phys. Lett. A 126, 459 (1988)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Alexander S. Mikhailov
    • 1
    • 2
  • Alexander Yu. Loskutov
    • 1
  1. 1.Department of PhysicsMoscow State UniversityMoscowUSSR
  2. 2.Institut für Theoretische Physik und SynergetikUniversität StuttgartStuttgart 80Fed. Rep. of Germany

Personalised recommendations