Maximum Entropy Approach for Stationary Response of Nonlinear Stochastic Oscillators

A new approach based on the maximum entropy method is developed for deriving the stationary probability density function of a stable nonlinear stochastic system. The technique is implemented by employing the density function with undetermined parameters from the entropy method and solving a set of algebraic moment equations from a nonlinear stochastic system for the unknown parameters. For a wide class of stochastic systems with given density functions, an explicit density function of the stochastic system perturbed by a nonlinear function of states and noises can be obtained. Three nonlinear oscillators are selected for illustrating the present scheme and the validity of the derived density functions is further supported by some exact solutions and Monte Carlo simulations.