Bifurcations in Asymptotically Autonomous Hamiltonian Systems Subject to Multiplicative Noise

The effect of multiplicative stochastic perturbations on Hamiltonian systems the plane is investigated. It assumed that fade with time and preserve a stable equilibrium limiting system. paper investigates bifurcations associated changes in stability appearance new stochastically states perturbed shown depending structure parameters decaying can remain or become unstable. In some intermediate cases, practical estimates for length interval justified. proposed analysis based combination averaging method construction Lyapunov functions.