The invariant density of a chaotic dynamical system with small noise (Q1808332)

The authors present the construction of an asymptotic expansion for the invariant probability density for the process defined by \[ dx= (\mu x-y^2+ 2z^2- \delta z) dt, \quad dy= y(x-1) dt+ \sqrt{2} \varepsilon dW, \quad dz= (\mu z+\delta x-2xz) dt \] where \(dW\) is the white noise and \(\varepsilon\) is a small parameter that determines the noise level. The asymptotic expansion allows to assess quantitatively the effect of noise, which is the source of substantial reducibility of the size of the chaotic invariant manifold.