Sensitivity analysis of stochastically forced Lorenz model cycles under period-doubling bifurcations

The problem of sensitivity for the limit cycles from the period doubling window of Lorenz model with respect to small stochastic disturbances is considered. Sensitivity analysis on the basis of quasipotential function is performed. Near to cycle the first approximation of quasipotential is an orbital quadratic form. Matrix of this quadratic form defined at all points of nonperturbed determined cycle (stochastic sensitivity function) is introduced as a base tool of a quantitative description for a system response on the external disturbances. Construction of sensitivity function is reduced to the solution of some boundary value problem for linear matrix differential Lyapunov equation. An iterative algorithm for numerical solution of this equation is suggested. The detailed investigation of multiscroll cycles of the Lorenz model on the basis of stochastic sensitivity function is presented. As shown, sensitivity function is the useful analytical tool for research of thin effects observed in stochastic Lorenz model near chaos in a period-doubling bifurcations zone.