Published: 31 December 2008

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

A. Naess1
E. Mo2
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Abstract

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

About this article

Received
19 September 2008
Accepted
02 December 2008
Published
31 December 2008
Keywords
chaotic attractor
additive noise
random phase modulation
path integration
probability density function