Path integration of the Duffing-Rayleigh oscillator subject to harmonic and stochastic excitations

This paper is focused on the Duffing-Rayleigh oscillator subject to harmonic and stochastic excitations using path integration based on the Gauss-Legendre integration scheme. First applying methods of harmonic balance and multiple scales to the deterministic case, the stabilities of the responses can be analyzed. Then the steady state periodic solution of probability density can be captured via path integration. At the same time, the changes of probability density induced by the intensities of harmonic and stochastic excitations are discussed in three cases.