Eur. Phys. J. B 83, 235-243 (2011)
https://doi.org/10.1140/epjb/e2011-20525-y

Symmetry breakdown of stochastic potential by noise cross-correlations among colored noise sources

Modeling of Complex Systems Dept., Sumy State University, 2, R. Korsakova Str., 40007 Sumy, Ukraine

Corresponding author: ^a knigorua@mail.ru

Received: 30 June 2011
Revised: 28 July 2011
Published online: 15 September 2011

Abstract

A nontrivial phenomenon in stochastic zero-dimensional systems, namely, the symmetry breakdown of stationary probability function due to the correlation between the noises is studied. As a model system to study this effect, we consider a generalized synergetic system of Lorenz type with Gaussian colored noise of each mode. In the frameworks of theoretical approximation and numerical simulations it is shown the fluctuation cross-correlations break the symmetry of bistable synergetic potential, producing an asymmetric effective potential. At that, cross-correlations play the twofold role: cross-correlations are the reason of symmetry breaking at small cross-correlation times on the one hand, and the reason of symmetry restoring at large values of cross-correlation times on the other hand. Moreover, it is shown that symmetry breakdown occurs only if one of multiplicative function is odd. Any other combinations of noises restore the symmetric form of potential.