Abstract
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.
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