Response of a duffing oscillator to combined deterministic harmonic and random excitation

The response of Duffing oscillator to combined deterministic harmonic and random excitation is investigated. The method of harmonic balance and the method of stochastic averaging are used to determine the response of the system. Theoretical analyses and numerical simulations show that when the intensity of the random excitation increases, the non-trivial steady state solution may change from a limit cycle to a diffused limit cycle. Under some conditions, the system may have two steady state solutions and jumps may exist.