Sensitivity analysis of stochastically forced quasiperiodic self-oscillations (Q2826975)

For a dynamical system with a two-dimensional toroidal attracting manifold the authors propose a new approach based on a stochastic sensitivity function. Using this function the authors approximate the quasipotential and probability density distribution of random states around the torus. The corresponding stochastic sensitivity matrix is a solution of a linear differential matrix equation. The authors derive a parametric description of the stochastic sensitivity function for the two-torus of a nonlinear system of stochastic differential equations. The case of a two-torus in three-dimensional space is studied. A computer-oriented algorithm for the calculation of the stochastic sensitivity of a two-torus is proposed. In the presented example a detailed parametric analysis of the stochastic sensitivity of a two-torus is given.