On the maximal Lyapunov exponent for a real noise parametrically excited co-dimension two bifurcation system. II
This paper continues Part I (see Zbl 0983.37063 above) deals with a codimension two bifurcation system driven by a small-intensity real noise process. Using an asymptotic analysis given by L. Arnold and the expression of the eigenvalue spectrum of the Fokker-Planck operator, the authors obtain both the asymptotic expansion of an invariant measure and the maximal Lyapunov exponent for the problems under consideration. Note that here only the situation in which the Lyapunov exponent \(\lambda_\varepsilon\) possesses an analytically explicit expression is investigated. Moreover in order to consider a rather general model, the real noise was assumed to be the output of a linear filter system -- a zero-mean stationary Gaussian diffusion process which satisfies a detailed balance condition. The results of the authors can be used to determine the stochastic bifurcation point with probability 1 for the relevant system.
scientific article; zbMATH DE number 1417800