Response of nonlinear oscillator to combined harmonic and random excitation

The resonance of Duffing oscillator to combined 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. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the intensity of the random excitation increase, the nontrivial seady state solution may change form a limit cycle to a diffused limit cycle. Under some conditions the system may have two steady state solutions and jumps may exits.