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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 52 (1988), S. 1005-1029 
    ISSN: 1572-9613
    Keywords: Noise in dynamic systems ; bifurcations ; Fokker-Planck equations ; degenerating parabolic-type equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract By an example of a two-dimensional hydrodynamic system, second-order Langevin equations with two correlated noise sources are investigated. It is shown that the asymptotic expression (t→∞) for the stationary distribution functionP depends on the order in which the limiting transitions;t→∞ andN 22→0 (N 22 is the power of one of the noises) are made. Using the method of local expansions in trigonometric form, approximate expressions are written for the distribution functionP at small but finiteN 22 tending atN 22→0 to the known exact solution.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1572-9613
    Keywords: White noise ; bifurcation ; dynamical systems ; hydrodynamic system ; Gaussian approximation ; functional-rational approximation ; stationary distribution function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The influence is considered of two additive correlated noise effects on a two-dimensional quadratic-nonlinear system describing the behavior of two hydrodynamic modes. Using the method of Gaussian approximation, local characteristics of the distribution function are calculated, which are used to construct the global distribution function with the aid of the method of fraction-rational approximations. It is shown that for a system at whose bifurcation point the asymptotic stability is lost, in an expanded space of parameters (bifurcation parameter in the absence of noise plus noise parameters) there appears an instability zone within which the stationary distribution function does not exist. The effect of noise correlation on the stationary characteristics of the system is studied.
    Type of Medium: Electronic Resource
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