A numerical study of the existence and stability of some chaotic attractors by path integration

The response of a harmonically excited Duffing oscillator with chaotic response is studied by replacing the excitation by harmonic excitation plus added noise, a harmonic motion with phase perturbations, and a narrow-band filtered noise. The mean frequency and excitation energy for all the models are the same, assuming that these are basic parameters for the response of the oscillator. The resulting probability densities in the state space show that the chaotic attractor is very stable for the different kinds of perturbations. Also, a new conditional path integration method is described, which is shown to be robust and accurate while the CPU time is kept at a minimum