高斯色噪声和谐波激励共同作用下耦合SD振子的混沌研究

As a typical oscillator with negative stiffness, coupled SD oscillator is widely used in engineering. At the same time, Gaussian colored noise exists widely in the external environment and may induce complex nonlinear dynamic behaviors, so its stochastic dynamic is a hot topic and difficult problem in nonlinear dynamics research. In this paper, the chaotic dynamics of bistable coupled SD oscillator under Gaussian colored noise and harmonic excitation are studied. The analytical expression of the homoclinic orbit of the coupled SD oscillator can not be given directly because its stiffness term is a transcendental function, which makes it difficult to analyze the chaos threshold. Firstly, the piecewise linearization approximation is used to fit the stiffness term of the oscillator, and stochastic Melnikov method for non-smooth system under Gaussian colored noise and harmonic excitation is developed. Based on random Melnikov process, then the chaos thresholds of the oscillator under weak noise and strong noise are obtained by the mean square criterion and the phase space flux function theory respectively, and the effect of noise intensity on chaotic dynamics is discussed. The results show that the chaotic region increases with the increase of noise intensity, that is, the increase of noise intensity is more likely to induce the coupled SD oscillator to produce chaos. When the damping is fixed, the chaos threshold decreases with the increase of noise intensity in the case of weak noise. However, the effect of noise intensity on chaos threshold is opposite for the case of strong noise. Finally, numerical results show that it is effective to study the chaos of coupled SD oscillator under Gaussian colored noise and harmonic excitation by the method in this paper. The results of this paper provide some theoretical guidance for the study of chaotic dynamics of stochastic non-smooth systems.