The response of Duffing oscillator to combined deterministic harmonic and r
andom excitation is investigated. The method of harmonic balance acid the m
ethod of stochastic averaging are used to determine the response of the sys
tem. Theoretical analyses and numerical simulations show that when the inte
nsity of the random excitation increases, the non-trivial steady state solu
tion may change from a limit cycle to a diffused limit cycle. Under some co
nditions, the system may have two steady state solutions and jumps may exis
t. (C) 2001 Academic Press.