ISSN:
1572-9613
Keywords:
Stochastic differential equations
;
Fokker-Planck equation
;
Hopf bifurcation
;
Liapunov functions
;
global stability
;
noise-induced transitions
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We prove analytically that additive and parametric (multiplicative) Gaussian distributed white noise, interpreted in either the Itô or Stratonovich formalism, induces global asymptotic stability in two prototypical dynamical systems designated as supercritical (the Landau equation) and subcritical, respectively. In both systems without noise, variation of a parameter leads to a switching between a single, globally stable steady state and multiple, locally stable steady states. With additive noise this switching is mirrored in the behavior of the extrema of probability densities at the same value of the parameter. However, parametric noise causes a noise-amplitude-dependent shift (postponement) in the parameter value at which the switching occurs. It is shown analytically that the density converges to a Dirac delta function when the solution of the Fokker-Planck equation is no longer normalizable.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01025992
Permalink
