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Academic Journal of Computing & Information Science, 2019, 2(1); doi: 10.25236/AJCIS.010016.

Chaotic motion of Duffing-Rayleigh oscillator under the Gaussian White Noise and stochastic harmonic excitations


Tao Xu, Xiao-shan Zhao, Ya Lu

Corresponding Author:
Tao Xu

Tianjin Univercity of Technology and Educatiaon, Tianjin 300222, China


In this article, we investigate the chaotic behavior of Duffing-Rayleigh oscillator under both the Gaussian White Noise and harmonic excitations. Applying the stochastic Melnikov technique, we obtain the necessary threshold conditions for chaotic motion of this deterministic system theoretically. Simultaneously, by the numerical simulation, the safe basins are introduced to show how the stochastic perturbation affects the safe basin when the Gaussian White Noise amplitude and harmonic excitation increase. The chaotic natures of the sample time series of the system are showed by the Lyapunov exponent and phase portrait maps. The results show that the safe basins appear fractal boundary under both the Gaussian White Noise and harmonic excitations.


Duffing-Rayleigh oscillator, Gaussian White Noise, harmonic excitation, fractal basin boundary, phase portrait, Lyapunov exponent

Cite This Paper

Tao Xu, Xiao-shan Zhao, Ya Lu, Chaotic motion of Duffing-Rayleigh oscillator under the Gaussian White Noise and stochastic harmonic excitations. Academic Journal of Computing & Information Science (2019) Vol. 2: 35-48. https://doi.org/10.25236/AJCIS.010016.


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