Consider a parameterized linear system in the Euclidean plane which is a rigid rotation for the critical parameter value. The Hopf bifurcation is a change of dynamics in a nonlinear perturbation of this system. One form of the stochastic Hopf bifurcation problem considers the perturbation of a system which undergoes Hopf bifurcation with a random field white in time. One method to study the stochastic Hopf bifurcation problem is the averaging method. To apply this method it is necessary to find the averaged SDE consistent with the covariance structure obtained by justify; LINE-HEIGHT: normal; MARGIN: 0cm 0cm 0pt" MSC : 15A23; 37H10; 40A30; 60B10; 60H10; 34C29; 60H35 Keywords : SDE , stochastic averaging , Brownian flow , n-point ge nerator , covariance structure, Cholesky decomposition, system of complex bilinear equations
